/sci/ - Science & Math

What are some applications of Bézout's theorem to basic projective geometry. Two degree one curves intersecting seems kind of trivial, since in a projective space anyways parallel lines will meet.

Ayyyyyy
How many things are emergent properties of the interactions of fundamental particles? (Eg distance, gravity)
Is there a lower level of reality than fundamental particles, and what is it?

Basically, what things are the results of the interaction/nature of fundamental particles, and how do you get from them to the thing that is an emergent property of them?

>>9622902
think I found a proposition: If [math]f(x,y)[/math] is a homogenous polynomial of degree [math]d[/math], then [math]Z(f)\subseteq \mathbb{F}P^{n}[/math] has at most [math]d[/math] points.
stinks of Bézout.

>>9622645
how did we get pictures from voyager?

>>9623055
Like this

https://www.youtube.com/watch?v=bS4jPjs6JPw

I wanted to get in a CompSci college but barely failed the exam and got redistributed in a traffic and transport college in the same uni ,my aunt who is a teacher at that uni (and teached me math and phys for the exam because I was a brainlet in highschool) and my family all told me it would be better to stay in that college after a year has passed so the year I spent there would not be wasted ,so I did ,even though I felt it was a huge mistake now almost two years later I feel like this degree can't get me a good rewarding job and that thought took all my motivation away I can't sleep and I feel like I don't have anything to get up in the morning for
So I want to ask should I quit this college and go for the compsci degree and a job in programming?And what's a good job that I can aim for with a traffic and transportation degree?

Why the fuck are trig Integrals so complicated

>>9623122
they aren't
just memorize reduction formulas

>>9623121
>Me programmer irl
You should be programming on your spare time. Learn programming on your own, then develop applications for traffic and transportation. Make simulations: read papers on algorithms for effecient traffic signals, and implement them. Going to college for it is pointless because if you're going to be a successful programmer, you need to be able to do it on your own.

You might not be intelligent enough to pick up programming. Its too complex for people who don't have a knack for it to be able to pick up easily and use proficiently. Give it a shot. You may realize that it's not what you want to do. It happens to a lot of people who get into CS.

>>9623267
That's what people tell me but to get a job you have to have some sort of certification people trust in and that HR recognizes how would I get that without a college?

>>9623202
>memorizing when Euler gave us [math]e^{ix} = \cos(x) + i\sin(x)[/math]
Engineer detected.

Theorically how much energy would it take to manipulate time?

>>9623121
look faggot, if you cant pass entrance exams you cant program.

>>9623793
to be fair it was a kind of math I haven't been teached and I almost got in

What are some good resources for learning R?

>>9623630
you _are_ manipulating time right now
you'll need a lot of energy to noticeably manipulate it though

suppose that [math]r\colon[a,b]\longrightarrow C[/math] is a parametrisation of a curve C and r* is the parametrisation of C in the opposite direction, that is r*(t)=r(a+b-t). Then what is [eqn]\int_C F\cdot dr^*\,?[/eqn]
I think it's [math]\displaystyle\int_a^b F(r(a+b-t))\cdot r'(a+b-t)dt[/math], which follows from the definition(?). but that's wrong and i cant see how it would be otherwise.

I begin the dreaded Series portion of calc 2 next week. What do you guys recommend to get an upper edge

>>9624001
Who "dreads" series? Series as a subject are way easier than antiderivatives.
There's like 4 or 5 convergence tests you have to know, just practice enough to develop a feeling for when each one works and the rest is autopilot.

>>9624001
be comfortable with simplifying factorials in different ways, learn each test, do a bunch of practice. it's really no worse than the rest of the course.

>>9623957
Think you're a minus sign off. See http://tutorial.math.lamar.edu/Classes/CalcIII/LineIntegralsPtI.aspx explanation above third green box

I need some form of strictly noncommutative algebra (i.e. a*b != b*a for all distinct (a,b)) for an proof attempt at representing combinatorical objects algebratically

The only noncommutative algebra I know of that can be calculated easily are matrices but they don't suit my needs. Are there any other such systems?

>>9624084
due to representation theory you're going to find matrices if you want regardless

Can anyone give me some links to me that prove IQ matters?

>>9624119
http://lmgtfy.com/?q=why+does+IQ+matter

How should I go about this?

>>9624243
There is something about vector analysis that is just so damn sexy.

>>9623957
>>9624039
sorry i just realised it's not clear from my question, but F is a vector field

>>9624243
What have you tried?

how do i prove that the intersection of two distinct planes is a straight line?
i've started by considering two distinct planes [math]n_1\cdot (x-x_0)=0\,,\quad n_2\cdot(x-x_0)=0[/math] where n1 x n2 is non-zero, but that's it, and idk how to proceed. I imagine the cross product will be involved since the direction of the line is ±n1 x n2, but can't think how to use it with where i am now

I think i could prove it by substituting n=(a,b,c), x0=(x0,y0,z0),... etc. and solving the two equations, but i'd prefer not to

>>9622645
Re learning math from the ground up and stuck on a problem.

5/16 • 1/10 - 1/32

The answer is 0, but I got 40/5 for some retarded reason.

>>9624376
>how do i prove that the intersection of two distinct planes is a straight line?
You can not, since it is not true.

>>9624379
wtf
what's a counterexample?
>>9624377
post how you got 40/5

>>9624384
>wtf
>what's a counterexample?
Draw some pictures of planes.

>>9624384
What is did I get the Least common denominator of 16, 10 and 32 and got 160.

5•10 50/160

1•10 10/160

1•5. 5/160

Then I multiplied 10/160 • 50/160
And got 500/160.

500/160 - 5/160 and got 495/160
Simplified that and now I’m at 99/32.

It’s a different answer but I’m still fucking up

>>9624409
I'm not sure where the 50/160, 10/160 and 5/160 came from, but the answer is
[math]\dfrac{5}{16}\cdot\dfrac{1}{10}=\dfrac{5\cdot 1}{10\cdot 16}=\color{blue}{\dfrac{5}{160}}[/math]

[math]\begin{align}\dfrac{5}{16}\cdot\dfrac{1}{10}-\dfrac{1}{32}&=\color{blue}{\dfrac{5}{160}}-\dfrac{1}{32}\\ &=\dfrac{5}{160}-\dfrac{5}{32\cdot 5}\\&=\dfrac{5}{160}-\dfrac{5}{160}\end{align}[/math]

>>9624409
I'm not sure where the 50/160, 10/160 and 5/160 came from, but the answer is
[math] \dfrac{5}{16}\cdot\dfrac{1}{10}=\dfrac{5\cdot 1}{10\cdot 16}=\color{blue}{\dfrac{5}{160}} [/math]

and then

[math] \begin{align}\dfrac{5}{16}\cdot\dfrac{1}{10}-\dfrac{1}{32}&=\color{blue}{\dfrac{5}{160}}-\dfrac{1}{32}\\ &=\dfrac{5}{160}-\dfrac{5}{32\cdot 5}\\&=\dfrac{5}{160}-\dfrac{5}{160}\end{align} [/math]

>>9624444
What I did is just find the least common factor of the three numbers and multiplied the numerator and denominator respectively then multiplied and subtracted.

I’m not sure why I did that.

When you did

5/160 - 1/32 why did you multiply by 5 ?
What’s the meaning behind that

>>9624444
Another thing I did is that instead of just multiplying I looked for a common denominator.

I didn’t know you only do that when you’re adding and subtracting fractions.

>>9624450
You can only subtract terms if they have the same denominator. So i multiplied the denominator by 5 since 32*5=160. The fraction is still the same though since i just multiplied by 1:
[math]\dfrac{1}{32}=\dfrac{1}{32}\cdot 1=\dfrac{1}{32}\cdot\dfrac{5}{5}=\dfrac{5}{32\cdot 5}[/math]

>>9624444
nice. how do you make it blue?

Can somebody explain how to find a formula for (x^n-1)/(x-1)?

>>9624505
>Can somebody explain how to find a formula for (x^n-1)/(x-1)?
https://en.wikipedia.org/wiki/Polynomial_long_division

>>9624513
Ok, I'm not trying to be a brainlet right now, but I still can't figure it out, how do I deal with the exponent being n?

>>9624577
>Ok, I'm not trying to be a brainlet right now, but I still can't figure it out, how do I deal with the exponent being n?
https://en.wikipedia.org/wiki/Mathematical_induction

>>9624581
So induction would be used to do the division?

>>9624577
Try it with n = 1, 2, 3, etc until you notice a pattern, then assume it's true for a general n and show how that assumption leads to it being true for n + 1.

The potato paradox.

100lbs of potato if it is 98% water and 1% solid stuff and by mathematics removing 2% of the water would mean it would weigh 98 lbs right? No! If you try out the math by solving it it always ends up with 98.89898989...% and that is wrong. Instead the right answer is it would weigh 48lbs and that's because if you divide it the answer would be "exactly" 98%.

How does removing 2% of a mass decrease it's weight over 50%.

Pls explain

>>9624620
[eqn]\sum\limits_{i=1}^n i^{n-1} = x^{n-1}+x^{n-2}+...+x^2+x+1[/eqn], would this be right for the formula?

>>9624650
The right hand side looks good but does not correspond to what you've written on the left.

>>9624672
Thanks, I see the issue

HAVN'T SLEPT FOR 30 HOURS
WENT THROUGH 400 PAGES OF LINEAR ALGEBRA BOOK
2 LITERS OF ENERGY DRINKS CONSUMED

>>9624687
You’ll forget it all for cramming

Why do we reduce to 9? Is this essentially just cross division to reduce to its lowest terms?

>>9624729
You can rewrite the top as (9)*1*11/(9)*4*44, the 9s cancel each other out.

>>9624742
Not quite understanding you

>>9624729
[math]\left(\frac{9\cdot11}{44\cdot36}\right)=\left(\frac{9}{36}\cdot\frac{11}{44}\right)[/math]

>>9624793
But 9•11 is 99? I’m definitely missing something here sorry

>>9624808
[math]\frac{9}{36}=\frac{9}{9\left(4\right)}[/math]

>>9624841
I’m too retarded, I’ll figure it out eventually thanks though

>>9624793
>>9624852
Wait are you just flipping the denominators and then just dividing the numerator and denominator?

So I am finishing up Real Analysis and thinking about being a teacher's assistant next semester for calc, but I have never learned integration by parts and my teacher keeps asking questions that need it/ What is the single best way to learn it?

>>9624861
you can do all other types of integration??

>>9624869
Pretty much, I self-studied them, but I hated doing integration by parts so I didn't practice it enough to learn it well.

When it says the subsapce given by the equation, does it mean the orthogonal complement of the vector (1,1,1)? That's what I assumed and when I worked it out I ended up with nice numbers typical of a contrived example question but I have a feeling i've been going in the complete wrong direction. I'll post my working in a sec in case it helps anyone

>>9624892
I'm a messy cunt sorry

>>9622645
/a/ was able to make a cripple fucking simulator. What have you done with your life?

Would /sci/ be interested in working with some autists from /g/ to develop a FOSS android? We're talking from the ground up - motor skills, intelligence, human interaction, and human "interaction". We were thinking /sci/ could especially help with materials science, but volunteers with any knowledge/skills/ambition are welcome.

Does anyone know of any YouTube videos to help a brainlet learn this stuff? I really want to understand it

What does it mean when a problem asks me to find the thermodynamic identity for a certain variable? I thought the thermodynamic identity was just dU = TdS - PdV.

About to finish my first two semesters for my 4 semesters MS (EE). I have the choice of a few internships over my subject at good companies or doing research at my university over the summer, should I just do the internship if I am not 100% on whether I want to pursue a PhD after my MS yet? I plan to go into industry whether I get an MS or PhD anyways.

What are some good freeware circuit drawing and/or simulation software for Mac OS X?
I tried Spice, which works fine for windows, but is absolute ass on Mac. No fucking icons, everything's done through keyboard shortcuts, and running a simulation is painful as all hell.
Any and all alternatives are welcome

>>9625002
Have ya tried Khan Academy?
https://www.khanacademy.org/math

>>9624729
Consider this:

[math]
\frac{2}{1} * \frac{1}{2} = 1
[/math]
essentially 2*1/2
so that's why we can simplify by reducing 2s

Shouldn't the directions on the middle spring be flipped? As in I push m to the right, middle spring is compressed; meanwhile push m2 to the right, resulting in a restoring force to the left in the middle spring

>>9624084
If b is a power of a you have a problem.

>>9624892
You are correct. You are basically subtracting out the mean of x y and z, giving you three new numbers having zero mean

>>9625391
>Shouldn't the directions on the middle spring be flipped?
no, you could flip the direction of the arrows if you wanted to, but then you would also have to change the sign of the equation
> As in I push m to the right, middle spring is compressed; meanwhile push m2 to the right, resulting in a restoring force to the left in the middle spring
the spring is only ever going to push the masses apart or pull the masses together, it doesn't make any sense for the spring to be pushing one and pulling the other

>>9624376
>how do i prove that the intersection of two distinct planes is a straight line?
You don't. Consider the case in which the planes are the same, or the case in which they are parallel.

Without thinking about it, my guess is that you consider a system of linear equations which describe where the planes are.
From that you will conclude that, either they intersect everywhere, have a one dimensional solution set, or there is no solution.

what's the proper definition of a linear ODE?
i've seen a lot of definitions like it's an ODE where "all y terms appear in a linear manner", "all y terms appear to a power no higher than 1", etc., but they confuse me and don't seem particularly rigorous

So I've got a particle theory module at uni that frequently uses Einstein summation, the spacetime metric, spacetime vectors and things like that. But despite mentioning lowering and raising indices like
[eqn]V^\mu=\eta^{\mu\nu}V_\nu[/eqn][eqn]V_\mu=\eta_{\mu\nu}V^\nu[/eqn]
It is never explained what the difference is between the index being above or below. It's not really explained what its even called so I have no idea what to google/youtube to learn more. Apparently I might want to raise or lower the indices to help simplify equations but I have zero intuition as to when or why I might do this

I think I'm retarded, max is supposed to be a non-linear function, but using the usual proof of linearity, it keeps coming up as linear. Is max() not what I think it is?(the highest value of a matrix)

>>9625761
surely the best way to prove this is to find a counter example?

>>9625771
It's just that I'm trying with different numbers and I'm getting the same result. Using max() on wolfram alpha also wields the same results, yet everywhere I see, they say that max() is nonlinear. As usual, I'm probably doing something wrong, and I don't know what.

>>9625761
>max is supposed to be a non-linear function
Why?

>>9625757
A subscript index is a covariant vector and a superscript is a contravariant vector.
They are different ways to discribe the same vector in non euclidean space.
You can read about it in every book about differential geometry and tensors, they will do a way better job explaining it than I could.

>>9625782
It isn't?

>>9625761
I got it, as usual, I'm dumb. the problem is that I kept using the same place to hold the highest number.

I read this article about the brain and it made me question a lot of things I assumed : https://aeon.co/essays/your-brain-does-not-process-information-and-it-is-not-a-computer
Do you anons find any value in it? If yes do any of you know some literature that I could read to have an understanding of how the human brain really functions? Can be a thesis or a book, anything to know more if theoretically you'd want to create a true artificial intelligence for example.
I know we are far from knowing enough to achieve that but I'd like to know were science currently is on the subject

>>9625274
So what you’re describing is cross cancellation?

>>9624243
[math]x_0=\gamma(0), x_\alpha^+=\gamma(\alpha), x_\alpha^-=\gamma(-\alpha)[/math], these three points define a circle, so you can write some equation and the center [math]c_\alpha[/math], then differentiate this equation and you get two zeroes, [math]y_1,y_2[/math], then differentiate again and you get a zero [math]z_0[/math], if [math]\alpha\rightarrow 0[/math] then all those points tend to [math]x_0[/math] and the equations tell you they satisfy exactly what you wanted in the limit, or something.
Been a while since I took differential geometry, often you just have to find the right equation and you get the result you want right away.

>>9625856
Well, the cross-cancellation is just a handy term but i dont think it is an actual thing.

Basically, if you multiple a number by X and then divide by X there is no point doing so, thus you can remove X's

>>9625799
Ahh thank you

hey a dumb physicist told me once that subzero temperatures (Celsius) are 'hot'. What did he mean by that??

What should I do if I am interested in CS but do not want to study baseline engineering?

What do you call this letter?

>>9625946
http://detexify.kirelabs.org/

>>9625946
xi
(pronounced "zee")

>>9625936
Study CS without studying baseline engineering

>>9625843
Does this not belong in this thread ? Should I make another one just for this ?

>>9625974
well it would certainly be better than the constant iq thread spam

>>9625936
Self teach yourself CS.

>tfw I had to watch youtube video to understand basic radiation dosimetry
Now I have become true Pajet

Should I put MATLAB as a language or software on my resume? I've never really "coded" with it in my eyes, just used it for matrix calculations, graphs, laser things, and as a big calculator basically

>>9623957
Your parametrization is a joke: try the parametrisation is r*(t)= r(b-t), where t goes from 0 to a.

Notice that the minus sign comes out of the derivative r'.

>>9624243
Notice that the positive curvature at 0 implies that it is not a point of inflexion, in particular, in a small neighbourhood of beta there exists a circle. You could show this by, say, doing a Taylor expansion of Beta around 0 up to second order.
Uniqueness is obvious. The rest comes from the first part.

can someone explain to me what the fuck a pullback of multilinear form represents

>>9622645
How many of you guys have taken the physics GRE? How is it overall? How much did you study for it?

I know it's mostly stuff from intro classes, so I'm gonna go back this summer (between sophomore and junior) and try to basically be able to recite Halliday, Resnick, and Walker in my sleep. But what did you guys do about the special topics that you might not have covered by the end of you're junior year.

Thanks boys and good luck.

>>9624243

Why you people don't just ask Alexa?

>>9624376

>>9624505

Does anyone know why when i measured the attenuation coefficient of optical fibre across varying wavelengths of light, my findings show shorter wavelengths (green LED 550nm) outperform longer wavelengths (IR LED 750nm) by an order of magnitude or more?

The reason i ask is that a little research has shown the most common wavelengths of light used in long distance fibre optic transmission are all in the IR range (850 nm, 1300 nm, and 1550 nm).

Any help would be greatly appreciated as all google wants to tell me is what i already know.

>>9626168
you should combine programming languages and software into 'IT skills'

>>9625953
it's 'ksee', friend

>>9626384
I took it last year. It's pretty gnarly. I studied for about two months prior. There's five practice tests available online. You gotta take all of those. Make flashcards based off of the questions you miss. There are also official flashcards online somewhere. Learn elimination strategies. This was my regimen and I got a 910. Good luck anon.

>>9623630
1/infinity
Any amount is enough.

>>9626507
Thanks man.

>>9624892


>>9624892

>>9626413
>>9626443
>>9626455
>>9626539
nice work anon

>>9626539
doesnt a matrix of orthogonal projection have to be its own square

Find the Σ0 → Λ0 transition matrix element < Λ0 ↑ | sumi=1 µi(σz)i|Σ0 ↑>. Express the results in terms of µu, µd, µs.

Our professor never went over how to transition between two baryons, and only used a similar technique for finding the protons magnetic moment. So I am very lost.

Is there something like the Luxel Body Badges but digital?
I need something that records cumulative dosage in mrem(dosimeter).
Rads and Gy are fine too as I can covert it manually if needed.

Trying to find good resources on [math] \sigma -[/math]compact sets that are not compact. I know that [math] \mathbb{R}^{n} [/math] satisfies the above, but I can't seem to find any other examples. How can I construct such metric spaces?

>>9626223
>Your parametrization is a joke: try the parametrisation is r*(t)= r(b-t), where t goes from 0 to a.
don't think it really matters. they're both the same and that's the one that was in the text. it also feels more natural to define the reverse parametrisation that way since r and r* have the same domain.
>Notice that the minus sign comes out of the derivative r'.
why though? i imagine it's the chain rule, but how exactly do i apply it there?

>>9626573
>>9626539
you are right sorry, i was in a hurry when i made that one

>>9624892
This time again, but correct, was in a hurry so didn't think right

>>9625034
usually you have to divide by dx where x is some variable, usually time, and then you use the definitions and maybe integrals to find the variable

>>9623957

>>9626751
thanks bud, does the method youre using have a name, we got the same answer but it looks a lot cleaner than my working

>>9626788
Well idk just logic i guess? Also note I wrote the map P the wrong way round in the pic lol.

How I thought of approaching the problem:

>I need to describe a linear map between R^3 and the subspace W
>the map has to project onto the subspace W
>any linear map can be described by its effect on the basis (of R^3)
>what does projection mean in this setting? Well, it means taking off the component of the vector that goes out of the plane
>The normal vector to the plane is the "purest" element that goes out of the plane (by definition) so I take that one
>Take a basis vector, and subtract the "normalness" out of it
>ok great, now I know how the projection acts on e_1, now i should calculate e_2 and e_3
>Every linear map has an associated matrix, call it A. Then Ae_1 = (what i calculated for e_1). Repeat for the other two and you can discern A.
In this case, since I could use the standard basis (and not just an arbitrary one), it is pretty easy to see what A is.

>>9626803
interesting, thanks for your help dood

ask more math question stupid anons

t. bored phd student

How do I go into evaluating [math]\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\rho{e}^{-\rho}sin\phi d\rho d\theta d\phi[/math] with all the ugly indeterminate forms?

>>9626907
this integral does not converge

>>9626907
what do you think it means to integrate dphi or dtheta from -infinity to infinity? Generally they are limited to 0 to 2pi and 0 to pi.
see pic

>>9626907
>-inf to inf
uh what are you doing

Plugging my /wsr/ thread. It's about identifying the name of a [thing] related to math and programming.

>>>/wsr/483076

Can someone explain why the dy/dx in partial notation is 0? This is for implicit differentiation btw

>>9627234
y doesn't depend on x

Optics or Materials science? Currently just doing BS in Physics, but plan to do PhD in the chosen field.

>>9627243
what does that mean desu? im dumb af can u explain

>>9627234
>>9627250
https://en.wikipedia.org/wiki/Partial_derivative#Geometry

See their example for a cone. In your case y(x,z)=y. i.e. it doesn't depend on x. Say for the unit circle y=+-sqrt(1-x^2), so y depends on x and its partial derivative is -x/sqrt(1-x^2)

>>9627258
so if it doesnt depend on x does that mean the partial change of y is 0?

>>9626944
>>9627001
Ok yeah I'm a retard, that makes sense. I also meant for the left half of the integrand to be rho^3 instead of just rho.

But when integrating by parts with respect to rho, I get
[math]\int_{0}^{\infty}{\rho}^{3}{e}^{-\rho}d\rho \rightarrow \left ( 0 \right ) + 3\int_{0}^{\infty}{\rho}^{2}{e}^{-\rho}d\rho \rightarrow (0) + 6\int_{0}^{\infty}\rho{e}^{-\rho}d\rho \rightarrow (0) + 6\int_{0}^{\infty}{e}^{-\rho}d\rho = 6[/math]

And then solving for the other two integrals, I get
[math]6\int_{0}^{\pi}\int_{0}^{2\pi}sin\phi d\theta d\phi \rightarrow 12\pi\int_{0}^{\pi}sin\phi d\phi = 24\pi[/math].

But the ((((((((textbook)))))))) says the answer is only [math]2\pi[/math]. So are the coefficients not actually part of the problem?

>>9626815
how much harder does calc 3 get after partial derivatives

and if possible, how much harder does phys 2 get after induction for magnetic fields

Is quora just a /sqt/ website?

Algebrists are useless monkeys.

Can anyone explain pic related to me?
I guess I understand a, b, c and d, but I'm lost at e.
is e just some illustration that does not have to be correct and you are actually required to multiply whatever functions are behind [math]g(\lambda)[/math] and [math]h(t-\lambda)[/math] and plot the result, or is there a graphical way to multiply to curves?
It looks like they are added, but if I measure it, it does not really fit, but multiplying the singe values is off way more.
I would think that there should be some graphical way (book's from the 60s where they did integrals by drawing them, cutting them out and wheighting the paper), but if there is, I can't find it.
Any help?

>>9622645
Not technically a science question but does anyone have the pic with Cauchy making an interjection about calculus?

>>9627591
Its just a schematic drawing showing the general principle of convolution. The Wikipedia page on it is actually quite good.
Convolution is almost always solved by Fourier transforms. Convolution in real space is multiplication in Fourier space.

>>9627591
You can approximately multiply curves if you know where y = 0 and y = 1 are, and know about the derivatives of the curves.
The graph in e isn't supposed to be exactly correct, it's just a qualitative thing. You can see that gh is about right, it has the right max and min, correct sign of the derivative, etc.

>>9627471
im not american so i did most of that in highschool /first year, but not very - unless you refrain from thinking: you most likely will need to set up 3D integrals and there's no general procedure to do it, although it's relatively easy for HW/exam problems to see the problem geometrically and understand that there's a canonical choice of parametrisation. This obviously will not make sense to you now, so I'll just say: think geometrically and not just think everything is algorithms.

As to phys 2 i have no clue what comes after but if its intro to modern physics (ie relativity and baby QM) then it's basically plug and chug integrals for the latter (easy shit), or just play around for the former.

>>9627635

>>9627648
>The graph in e isn't supposed to be exactly correct, it's just a qualitative thing.
Thought as much, but I thought (hoped…) that you could simply multiply curves graphically, and the shown graph is quite close to a graphical addition, which seemed off to me.

>>9625954
It's not possible in my country i.e. India

I'm hypoglycemic. Why do I feel drunk when I have low blood sugar? I make terrible decisions and easily get angry. What's going on in my brain?

Is there any easy way to prove addition is commutative in PA without using induction?

>>9622645
I have difficulty when it comes to figuring problems like these. I don't feel confident in my ability to convert the given information to a quadratic equation. Is that indicative of poor critical thinking skills? If so, is that something which can be improved? Any recommendations on how?

>>9627888
What the solution for this?
i was trying linear function but clearly it isnt,

>>9626028
Wow this is really shit.

>>9627888
>>9627923
i reckon
[math]R(t)=t\cdot(9500+(14-t)\cdot 1000)\,,\quad 8.5\leq t\leq 23.5[/math]

first you know that revenue is the ticket price * attendance so you have something like Rev(t)=A*t . Then attendance is dependent on ticket price so you need to find A(t)

>>9627949
Ok that makes sense, does not look so hard.

Is it Calculus?

>>9627760
can't you really study something if you're not paying for fucking tuition fees you dumb pajeet fuck

>>9627923
Yeah it's a quadratic
>>9627949
Here's the solution the book arrived at

>>9628046
Oh interesting

I'm not good at this stuff but I really like it

>>9627471
Double/triple integration wasn’t that bad. Coordinate changes (polar, cylindrical, spherical, jacobians etc) might take some thinking, but if you study it should come.

At my uni, multivariable calc (intro to R^3, vector parameterizations, partial differentiation, multiple integraton) and vector calc (vector fields, jacobians, line/surface integrals, greens/stokes/divergence theorems) are split up into Calc 3 and 4 respectively. I’ve struggled way more in calc 4 desu, but I haven’t besn studying nearly as much as I should be.

given
[math]3a^2bc[/math] where a = -2
how are we supposed to do it?

3 * (-2)^2 or 3 * (-2^2)

>>9628167
Whenever there’s an exponent greater than 1, the sign of its coefficient is the sign of the final result. All other signs are ignored.

So if a was positive, it would be 3(a^2)(absolute value of b)(absolute value of c) and if a was negative it would be -3((absolute value of a)^2)(absolute value of b)(absolute value of c)

>>9628331
Are you sure you've read my question correctly?

I'm not asking what is the final sign on the monomial, I'm asking what the rule is here to calculate exponent and it's base:

why is
[math]3a^2bc[/math]
for a = -2
is
[math]3(-2)^2bc[/math]
and not
[math]3(-2^2)bc[/math]
because it would be a different sign in second case and the question is why are we taking only base in parenthesis

What state of matter is electromagnetic radiation? Like gamma rays, are they solid liquids or gases

Is there a strictly mathematical definition for flux in a vector field?

>>9628349
They aren't even matter

>>9628349
you answered your own question

>>9628349
hint: they're the state that = MC^2

>>9627957
not to get that answer, no.
maybe if you wanted to find the optimal value you could use calculus, although you don't really need to

>>9628481
I mean quadratic functions part of what mathematics's discipline? What are you strudying right now.

Why is [math]\sqrt{3}^3=3\sqrt{3}[/math]? Afaik

>>9628498
Because [math]3=\sqrt{3}^2[/math].

>>9628358
[math]\displaystyle\iint\limits_SF\cdot n\,\mathrm{d}S[/math] ?

>>9628484
>quadratic functions part of what mathematics's discipline
precalculus? im not sure what youre asking. also i'm not >>9627888

Can any linear transformation be written as a rotation followed by a translation?

if the speed of light is constant how can there be red and blue shift?
Or is it due to the relative speed increasing/decreasing

>>9628594
Translations are not linear, you're thinking of affine linear. But if you bend your question in one, two places, then the answer is yes. Also please consider

https://en.wikipedia.org/wiki/Singular-value_decomposition

>>9628594
No. Scale and shear are also linear transformations. And translation isn't actually a linear transformation, it's affine (although you can effectively make it linear by using homogeneous coordinates).

>>9628498
what is [eqn]\sqrt{3}*\sqrt{3}[/eqn]?
Just 3.
Now, you still have one [eqn]\sqrt{3}[/eqn] left over, but you can't find the square root of a prime number.
hence, [eqn]3\sqrt3[/eqn]

>>9624119

It doesn't.

You're just looking for a numerical validation of your intelligence because you probably doubt yourself, which is fucking stupid. Everyone has tremendous mental capabilities waiting to be unlocked, it's mostly a matter of interest and motivation that steers people one way or the other. Everyone getting worked up over a demonstrably bad metric for "Measuring" intelligence is wasting their time and should spend it doing other things, like improving their own knowledge or the knowledge of others.

>>9628594
No, for example a projection onto an axis is linear but isn't a rotation.

>>9628637
Because the universe is expanding the light waves get stretched out as they travel

>>9627804
Glucose is the brain’s fuel source. Without a sufficient fuel source, neurotransmission is impaired and you experience the symptoms you described.

For example, the “drunken” feeling is ataxia, and it’s because your cerebellum can’t communicate properly with the rest of your nervous system. It’s impairing your sense of balance and coordination.

>tfw too scared to go to office hours because I don't want to look dumb
How do I stop being such a faggot?

>>9628687
your professor went to office hours, why can't you

Should I quit my CS major?
To start off I have an extremely hard time with math because my memory is really bad (it affects my social life, and I have to relearn basic concepts every semester (for example I can't remember how to find the area of a circle let alone trig identities))
well now I'm in Calc 2 after taking 3 semesters of calc 1 to pass with a low C, and it is extremely hard for me, my highest grade so far was a 66%, and to make it worse we will never be allowed to use calculators again since some dude cheated in another class with one. am I wasting my time in this degree?

>>9628683
The mental symptoms (irritability, poor decision making) are due to a lack of available energy for communication between different parts of your brain. It’s spending the available glucose on vital functions such as circulatory and respiratory regulation. This leaves little available fuel for higher brain activity such as reasoning and mood regulation.

>>9628687
Note that office hours are actually used for networking.
It will benefit you in the long run if you are socially capable.

>>9628693
no youre not wasting time. you can become a programmer without math.

are you really stressed or anxious? what is making things hard to learn?

>>9628704
what if it's your prof who's socially incapable

>>9628711
my memory is making it hard. I have always had a really bad memory, so when I have to tackle all of the problems in calc 2 where a shit ton of old stuff comes back, stuff is reused, and it's assumed that it is common knowledge stuff I have a hard time because I have literally no idea what they are talking about since I completely forgot it.
it doesn't help that my professor doesn't really teach he just writes problems on the board and then asks how we should solve it (sometimes when he asks he isn't just saying it because he want's us to find the answer it's because he actually doesn't know(he'll tell us to use slader to figure it out some times))

>>9628716
Ive only met one like that over 6 years of studies so it is unlikely.
And even then things can be done with enough persistence.

Can someone explain percentages to me? I don't think they're real, or that they hold any real significance.

>>9628716
>>9628722
My coworker had a socially inept phd advisor.

He took her to conferences and didn't even introduce her to anyone, just went off and talked to the scientists in her field that she could've networked with.

She may just be bullshitting me though and have been too shy herself to go up and introduce herself with him there. She's a bit socially unobservant at times

>>9628725
that's because they're not real
they're extensions of the real numbers to allow mathematical operations on the square roots of negative numbers, known as "imaginary numbers"

>>9628743
>>9628725
percent(age) has nothing to dowith imaginary number tho?

>>9628764
the fuck are you on about

Do you know any webshop that sells US wines and ships them to the EU? All the shops I found so far don't ship overseas, and I need to buy two bottles of a specific Californian wine.

Is there an easy way to tell if a complex function is differentiable?
With a real function it is relatively easy to tell by seeing that it is continuous and has no "sharp points", but there is no such way to plot complex functions so this doesnt work.
Is there something similar?

For example is there a way to tell which of pic related is differentiable?

>>9628866
Please don’t support the People’s Democratic Republic of California thanks

>>9628932
But that variety is grown in Napa Valley... I need that specific one.

>>9628911
do you mean differentiable or holomorphic? Regardless, you're not going to be able to tell in general because you need a 4D image. Best test for holomorphicity is cauchy riemann i guess

>>9628725
Not sure what context you're looking for here, but per cent literally means out of a hundred, it's just a way to express things.

>>9628641
>>9628661

When I said translation, I guess I meant "scaling". For instance, if I want to scale the x component of a 2D vector by [math] \alpha [/math] and the y component by [math] \beta [/math], wouldn't the matrix that corresponds to this transformation be:

[math]\begin{align} \hat{T}(\alpha, \beta) = \begin{bmatrix} \alpha & 0 \\ 0 & \beta \end{bmatrix} \end{align}[/math]

And if the rotation by [math] \theta [/math] is:

[math] \begin{align} \hat{R}(\theta) = \begin{bmatrix} \cos \theta && \sin \theta \\ -\sin \theta && \cos \theta \end{bmatrix} \end{align} [/math]

It's clear that [math] \hat{T}(\alpha, \beta) [/math] does not commute with [math] \hat{R}(\alpha, \beta) [/math]. But I can't seem to be able to see how would the order matter ("scaling" and then rotating or rotating and then "scaling") nor can I see how wouldn't any linear transformation wouldn't be just rotations followed by "scalings". Also, isn't a shear a kind of rotation coupled with a scaling? Sorry if I'm being a brainlet.

>>9628667

In this case, the angle would just be 0 and [math] \hat{R}(\theta) [/math] would be the identity matrix.

>>9628932
>Cali most productive state with most workers rights, biggest economy, schools so good theyre unofficial ivys
no wonder right wingers hate it. jealousy is a bitch

>>9629150
>unofficial ivys
lol

is there a way to improve short term memory at 23?
I see people that can remember 20 sequential items and I can barely remember 8 on a good day.
Is it genetic?

>>9629239
Yeah don't compare our schools to those trash factories. Ivy league schools are literally just a brand and don't do much real shit.

>>9622968
>>9622973
Ree no one answered

>>9629388
True. If your career entails running a ball down a field cali schools can’t be beat.

Lads, how do I calculate C here? I have no fucking clue, also the fuck is Vj?

>>9629885
>Lads, how do I calculate C here?
Using the definition of c_{ij}.

>I have no fucking clue, also the fuck is Vj?
Reread the image.

Any anon that can help me to get a book on
>combinatorics, through a rigorous approach
>learning how to deal with sequences and convergence
>ruler-and-compass construction (my autistic intro to geometry prof loves this stuff for some reason)
>cool math problems, I already got Problem-Solving Strategies by Engel and The Art of Craft and Problem Solving

Is there a proof technique where you assume the claim itself is true and prove it for cherry-picked cases of contradiction that are sufficient?

I'm working on proving matrices with nonzero determinants are invertible.
>I.e. if matrix invertible then it has nonzero determinant
So I wanna say assume the claim is true. Then it must be the case that the statement "If a matrix is invertible then the determinant is zero and if a matrix is not invertible then the determinant is not zero" is false.

>>9629945
>Is there a proof technique where you assume the claim itself is true
No.

Okay, so, let me see if I understand it. A given sequence is convergent if it's monotonic and bounded. It's easy to prove if it's monotonic. But on god how can I prove that a given sequence is bounded/not bounded? Via induction?

For instance, how can I prove that [math]\sqrt{n}[/math] is not bounded? My guess is by contradiction, but I don't get it,

On the other hand, how can you prove that [math](1+\frac{1}{n})^n < 100 [/math], for instance?

>>9630029
>For instance, how can I prove that n√ is not bounded? My guess is by contradiction, but I don't get it,
for all c>0, c^2+1>c^2 implies sqrt(c^2+1)>sqrt(c)=c, so no upper bound

>>9630051
>sqrt(c^2+1)>sqrt(c)=c
sqrt(c^2+1)>sqrt(c^2)=c

>>9629945
>Is there a proof technique where you assume the claim itself is true and prove it for cherry-picked cases of contradiction that are sufficient?
No.

Considering your previous knowledge the proof might also be trivial, if you know about multiplication of determinants you are pretty much done.

can someone post math curriculum copypasta? high school freshman senior etc

>>9630347
>can someone post math curriculum copypasta?
Gladly.

High School:
• Euclidean geometry, complex numbers, scalar multiplication, Cauchy-Bunyakovskii inequality. Introduction to quantum mechanics (Kostrikin-Manin). Groups of transformations of a plane and space. Derivation of trigonometric identities. Geometry on the upper half-plane (Lobachevsky). Properties of inversion. The action of fractional-linear transformations.
• Rings, fields. Linear algebra, finite groups, Galois theory. Proof of Abel's theorem. Basis, rank, determinants, classical Lie groups. Dedekind cuts. Construction of real and complex numbers. Definition of the tensor product of vector spaces.
• Set theory. Zorn's lemma. Completely ordered sets. Cauchy-Hamel basis. Cantor-Bernstein theorem.
• Metric spaces. Set-theoretic topology (definition of continuous mappings, compactness, proper mappings). Definition of compactness in terms of convergent sequences for spaces with a countable base. Homotopy, fundamental group, homotopy equivalence.
• p-adic numbers, Ostrovsky's theorem, multiplication and division of p-adic numbers by hand.
• Differentiation, integration, Newton-Leibniz formula. Delta-epsilon formalism.

>>9630366
Freshman:
• Analysis in R^n. Differential of a mapping. Contraction mapping lemma. Implicit function theorem. The Riemann-Lebesgue integral. ("Analysis" by Laurent Schwartz, "Analysis" by Zorich, "Theorems and Problems in Functional Analysis" by Kirillov-Gvishiani)
• Hilbert spaces, Banach spaces (definition). The existence of a basis in a Hilbert space. Continuous and discontinuous linear operators. Continuity criteria. Examples of compact operators. ("Analysis" by Laurent Schwartz, "Analysis" by Zorich, "Theorems and Problems in Functional Analysis" by Kirillov-Gvishiani)
• Smooth manifolds, submersions, immersions, Sard's theorem. The partition of unity. Differential topology (Milnor-Wallace). Transversality. Degree of mapping as a topological invariant.
• Differential forms, the de Rham operator, the Stokes theorem, the Maxwell equation of the electromagnetic field. The Gauss-Ostrogradsky theorem as a particular example.
• Complex analysis of one variable (according to the book of Henri Cartan or the first volume of Shabat). Contour integrals, Cauchy's formula, Riemann's theorem on mappings from any simply-connected subset C to a circle, the extension theorem, Little Picard Theorem. Multivalued functions (for example, the logarithm).
• The theory of categories, definition, functors, equivalences, adjoint functors (Mac Lane, Categories for the working mathematician, Gelfand-Manin, first chapter).
• Groups and Lie algebras. Lie groups. Lie algebras as their linearizations. Universal enveloping algebra, Poincaré-Birkhoff-Witt theorem. Free Lie algebras. The Campbell-Hausdorff series and the construction of a Lie group by its algebra (yellow Serre, first half).

>>9630367
Sophomore:
• Algebraic topology (Fuchs-Fomenko). Cohomology (simplicial, singular, de Rham), their equivalence, Poincaré duality, homotopy groups. Dimension. Fibrations (in the sense of Serre), spectral sequences (Mishchenko, "Vector bundles ...").
• Computation of the cohomology of classical Lie groups and projective spaces.
• Vector bundles, connectivity, Gauss-Bonnet formula, Euler, Chern, Pontryagin, Stiefel-Whitney classes. Multiplicativity of Chern characteristic. Classifying spaces ("Characteristic Classes", Milnor and Stasheff).
• Differential geometry. The Levi-Civita connection, curvature, algebraic and differential identities of Bianchi. Killing fields. Gaussian curvature of a two-dimensional Riemannian manifold. Cellular decomposition of loop space in terms of geodesics. The Morse theory on loop space (Milnor's Morse Theory and Arthur Besse's Einstein Manifolds). Principal bundles and connections on them.
• Commutative algebra (Atiyah-MacDonald). Noetherian rings, Krull dimension, Nakayama lemma, adic completion, integrally closed, discrete valuation rings. Flat modules, local criterion of flatness.
• The Beginning of Algebraic Geometry. (The first chapter of Hartshorne or Shafarevich or green Mumford). Affine varieties, projective varieties, projective morphisms, the image of a projective variety is projective (via resultants). Sheaves. Zariski topology. Algebraic manifold as a ringed space. Hilbert's Nullstellensatz. Spectrum of a ring.
• Introduction to homological algebra. Ext, Tor groups for modules over a ring, resolvents, projective and injective modules (Atiyah-MacDonald). Construction of injective modules. Grothendieck Duality (from the book Springer Lecture Notes in Math, Grothendieck Duality, numbers 21 and 40).
• Number theory; Local and global fields, discriminant, norm, group of ideal classes (blue book of Cassels and Frohlich).

>>9630368
Sophomore (cont):
• Reductive groups, root systems, representations of semisimple groups, weights, Killing form. Groups generated by reflections, their classification. Cohomology of Lie algebras. Computing cohomology in terms of invariant forms. Singular cohomology of a compact Lie group and the cohomology of its algebra. Invariants of classical Lie groups. (Yellow Serre, the second half, Hermann Weyl, "The Classical Groups: Their Invariants and Representations"). Constructions of special Lie groups. Hopf algebras. Quantum groups (definition).

Junior:
• K-theory as a cohomology functor, Bott periodicity, Clifford algebras. Spinors (Atiyah's book "K-Theory" or AS Mishchenko "Vector bundles and their applications"). Spectra. Eilenberg-MacLane Spaces. Infinite loop spaces (according to the book of Switzer or the yellow book of Adams or Adams "Lectures on generalized cohomology", 1972).
• Differential operators, pseudodifferential operators, symbol, elliptic operators. Properties of the Laplace operator. Self-adjoint operators with discrete spectrum. The Green's operator and applications to the Hodge theory on Riemannian manifolds. Quantum mechanics. (R. Wells's book on analysis or Mishchenko "Vector bundles and their application").
• The index formula (Atiyah-Bott-Patodi, Mishchenko), the Riemann-Roch formula. The zeta function of an operator with a discrete spectrum and its asymptotics.
• Homological algebra (Gel'fand-Manin, all chapters except the last chapter). Cohomology of sheaves, derived categories, triangulated categories, derived functor, spectral sequence of a double complex. The composition of triangulated functors and the corresponding spectral sequence. Verdier's duality. The formalism of the six functors and the perverse sheaves.

>>9630370
Junior (cont):
• Algebraic geometry of schemes, schemes over a ring, projective spectra, derivatives of a function, Serre duality, coherent sheaves, base change. Proper and separable schemes, a valuation criterion for properness and separability (Hartshorne). Functors, representability, moduli spaces. Direct and inverse images of sheaves, higher direct images. With proper mapping, higher direct images are coherent.
• Cohomological methods in algebraic geometry, semicontinuity of cohomology, Zariski's connectedness theorem, Stein factorization.
• Kähler manifolds, Lefschetz's theorem, Hodge theory, Kodaira's relations, properties of the Laplace operator (chapter zero of Griffiths-Harris, is clearly presented in the book by André Weil, "Kähler manifolds"). Hermitian bundles. Line bundles and their curvature. Line bundles with positive curvature. Kodaira-Nakano's theorem on the vanishing of cohomology (Griffiths-Harris).
• Holonomy, the Ambrose-Singer theorem, special holonomies, the classification of holonomies, Calabi-Yau manifolds, Hyperkähler manifolds, the Calabi-Yau theorem.
• Spinors on manifolds, Dirac operator, Ricci curvature, Weizenbeck-Lichnerovich formula, Bochner's theorem. Bogomolov's theorem on the decomposition of manifolds with zero canonical class (Arthur Besse, "Einstein varieties").
• Tate cohomology and class field theory (Cassels-Fröhlich, blue book). Calculation of the quotient group of a Galois group of a number field by the commutator. The Brauer Group and its applications.
• Ergodic theory. Ergodicity of billiards.
• Complex curves, pseudoconformal mappings, Teichmüller spaces, Ahlfors-Bers theory (according to Ahlfors's thin book).

>>9630372
Senior:
• Rational and profinite homotopy type. The nerve of the etale covering of the cellular space is homotopically equivalent to its profinite type. Topological definition of etale cohomology. Action of the Galois group on the profinite homotopy type (Sullivan, "Geometric topology").
• Etale cohomology in algebraic geometry, comparison functor, Henselian rings, geometric points. Base change. Any smooth manifold over a field locally in the etale topology is isomorphic to A^n. The etale fundamental group (Milne, Danilov's review from VINITI and SGA 4 1/2, Deligne's first article).
• Elliptic curves, j-invariant, automorphic forms, Taniyama-Weil conjecture and its applications to number theory (Fermat's theorem).
• Rational homotopies (according to the last chapter of Gel'fand-Manin's book or Griffiths-Morgan-Long-Sullivan's article). Massey operations and rational homotopy type. Vanishing Massey operations on a Kahler manifold.
• Chevalley groups, their generators and relations (according to Steinberg's book). Calculation of the group K_2 from the field (Milnor, Algebraic K-Theory).
• Quillen's algebraic K-theory, BGL^+ and Q-construction (Suslin's review in the 25th volume of VINITI, Quillen's lectures - Lecture Notes in Math. 341).
• Complex analytic manifolds, coherent sheaves, Oka's coherence theorem, Hilbert's nullstellensatz for ideals in a sheaf of holomorphic functions. Noetherian ring of germs of holomorphic functions, Weierstrass's theorem on division, Weierstrass's preparation theorem. The Branched Cover Theorem. The Grauert-Remmert theorem (the image of a compact analytic space under a holomorphic morphism is analytic). Hartogs' theorem on the extension of an analytic function. The multidimensional Cauchy formula and its applications (the uniform limit of holomorphic functions is holomorphic).

>>9630373
Specialist: (Fifth year of College):
• The Kodaira-Spencer theory. Deformations of the manifold and solutions of the Maurer-Cartan equation. Maurer-Cartan solvability and Massey operations on the DG-Lie algebra of the cohomology of vector fields. The moduli spaces and their finite dimensionality (see Kontsevich's lectures, or Kodaira's collected works). Bogomolov-Tian-Todorov theorem on deformations of Calabi-Yau.
• Symplectic reduction. The momentum map. The Kempf-Ness theorem.
• Deformations of coherent sheaves and fiber bundles in algebraic geometry. Geometric theory of invariants. The moduli space of bundles on a curve. Stability. The compactifications of Uhlenbeck, Gieseker and Maruyama. The geometric theory of invariants is symplectic reduction (the third edition of Mumford's Geometric Invariant Theory, applications of Francis Kirwan).
• Instantons in four-dimensional geometry. Donaldson's theory. Donaldson's Invariants. Instantons on Kähler surfaces.
• Geometry of complex surfaces. Classification of Kodaira, Kähler and non-Kähler surfaces, Hilbert scheme of points on a surface. The criterion of Castelnuovo-Enriques, the Riemann-Roch formula, the Bogomolov-Miyaoka-Yau inequality. Relations between the numerical invariants of the surface. Elliptic surfaces, Kummer surface, surfaces of type K3 and Enriques.
• Elements of the Mori program: the Kawamata-Viehweg vanishing theorem, theorems on base point freeness, Mori's Cone Theorem (Clemens-Kollar-Mori, "Higher dimensional complex geometry" plus the not translated Kollar-Mori and Kawamata-Matsuki-Masuda).
• Stable bundles as instantons. Yang-Mills equation on a Kahler manifold. The Donaldson-Uhlenbeck-Yau theorem on Yang-Mills metrics on a stable bundle. Its interpretation in terms of symplectic reduction. Stable bundles and instantons on hyper-Kähler manifolds; An explicit solution of the Maurer-Cartan equation in terms of the Green operator.

>>9630374
Specialist (cont):
• Pseudoholomorphic curves on a symplectic manifold. Gromov-Witten invariants. Quantum cohomology. Mirror hypothesis and its interpretation. The structure of the symplectomorphism group (according to the article of Kontsevich-Manin, Polterovich's book "Symplectic geometry", the green book on pseudoholomorphic curves and lecture notes by McDuff and Salamon)
• Complex spinors, the Seiberg-Witten equation, Seiberg-Witten invariants. Why the Seiberg-Witten invariants are equal to the Gromov-Witten invariants.
• Hyperkähler reduction. Flat bundles and the Yang-Mills equation. Hyperkähler structure on the moduli space of flat bundles (Hitchin-Simpson).
• Mixed Hodge structures. Mixed Hodge structures on the cohomology of an algebraic variety. Mixed Hodge structures on the Maltsev completion of the fundamental group. Variations of mixed Hodge structures. The nilpotent orbit theorem. The SL(2)-orbit theorem. Closed and vanishing cycles. The exact sequence of Clemens-Schmid (Griffiths red book "Transcendental methods in algebraic geometry").
• Non-Abelian Hodge theory. Variations of Hodge structures as fixed points of C^*-actions on the moduli space of Higgs bundles (Simpson's thesis).
• Weil conjectures and their proof. l-adic sheaves, perverse sheaves, Frobenius automorphism, weights, the purity theorem (Beilinson, Bernstein, Deligne, plus Deligne, Weil conjectures II)
• The quantitative algebraic topology of Gromov, (Gromov "Metric structures for Riemannian and non-Riemannian spaces"). Gromov-Hausdorff metric, the precompactness of a set of metric spaces, hyperbolic manifolds and hyperbolic groups, harmonic mappings into hyperbolic spaces, the proof of Mostow's rigidity theorem (two compact Kählerian manifolds covered by the same symmetric space X of negative curvature are isometric if their fundamental groups are isomorphic, and dim X> 1).
• Varieties of general type, Kobayashi and Bergman metrics, analytic rigidity (Siu)

>>9628911
You can tell by looking that it’s not holomorphic. The lines in the left meet at right angles but on the right they don’t. If it were locally differentiable it would be locally conformal, I.e angle preserving

>calls maths, "math"
>doesn't call physics, "physic"

why are burgers so inconsistent, lads?

>>9630366
Do you have any book recommendation for the high school and freshman level?

>>9630654
The freshman section already has several textbooks and their authors listed in the parentheses, but for the high school level the topics have such standard treatments that any should do. Kostrikin-Manin's "Linear Algebra and Geometry" is referred to (first point), pic related and Stillwell's "Naive Lie Theory" (second point), Kolmogorov/Fomin (third and fourth points), Gouvea's book "p-adic numbers" makes for a friendly introduction (fifth point)

>>9630675
Sorry, skimmed and didn't see the textbooks.

Thanks!

Is energy real?
My physics professor explained that energy is just a mathematical construct we use to compute other stuff and that it doesn't really exist. Is this bs?

>>9625068
Internship

>>9625805
It is. Heuristic functions like max are nonlinear

Hey brainlet here. Can someone explain this to me ? https://youtu.be/xx9Q8PphAVo?t=796

why does water boiling at higher temperature causes the locomotive to steam up much slower ?

>>9630710
What do you mean by real?
Id say yes it is real. It is a mathematical tool. In addition, you can place your hand near fire and feel heat energy. You can hold an apple in your hand above the ground and the apple has potential energy.
In what sense would it not be real?

>>9626488
Check your results. Most attenuation spectra show the opposite result, hence why longer wavelengths are primarily used (as you noted)

>>9630124
It's just a lot to typeset and I was feeling really lazy so I kind of wanted to cheese it. I ended up going with elementary matrix multiplication anyways
>Determinant multiplication
I feel like a moron now

Question about physics
Now I am not quite sure if I fully understand how torque work...but let me ask:
When you are biking(assuming that you are biking forward), does the torque pull your bike a little bit to the left?
Or was it angular momentum?

Would a 10m EMR wave hitting a 9/10/11m wide object act the same as a 100nm EMR wave hitting a 90/100/110nm object? Even if the ratio is the same, does size dictate other factors? I'm not a scienceman, I just think it would be cool to know.

>>9630751
What youre feeling when you touch the fire is not energy itseld but the increased speed of the vibrations in atoms in your hand (put simply) so youre not feeling \emph{energy} per se. If you increase the height of an object relative to the ground then youre not giving it more energy, what youre simply saying is gravity will have more time to act upon it so its final speed will be higher. Thats what Im trying to say, its not a real thing, its a tool we use to simplify the math and the explanations for some phenomena.
This is my understanding of this, I may be wrong but I find this interesting.

I have some significant holes in my mathematics and have been able to perform quite well in my elementary math courses (Calc I - II, Diff Eq) but would like to fix these gaps since I want to have a better understanding of what I am doing and plan on applying to the math major. This summer I am probably going to be working as well as taking Calc III and Linear Algebra . Would it be possible to read Lang from cover to cover if I start now and set a deadline by the end of the summer? Or should I just prioritize topics that I lack knowledge on the most and then slowly read the rest of the book?

For what is highlighted, would it not be enough to just say that since it is true that au+v is in U for all v,u in U and a in F, it is true in the particular case when v=0?

>>9631124
Hey, I was like you.

Honestly, don't worry too much about it if you're doing well in your classes so far. What will end up happening as a math major is you'll go on and take rigorous classes like Real Analysis and Abstract Algebra, and you'll rigorously redo a lot of shit youre missing on. So you gaps will get filled in regardless. I was like you and did fine throughout calculus and the like.

Only thing I would say is pay attention to developing your geometric intuition. That shit keeps coming up

>Dice Game 50/50 winning Chance
>100.000 draws
How likely is it that I lose 17 times in a row ?

>>9630930
The torque you create on the downward stroke of your pedalling tilts the bike to the same side as the stroke, so it pulls both left and right as you pedal.

>>9631239
No, because they didn't specify that the subset included 0, the criterion obviously ensures it though.

>>9624444
Checked

>>9631271
WAIT
Its 17/100.000
Am I right ?

>>9631326
No, it's (100.000-16)/2^17~0,76

>>9631336
This doesn't even make sense.

>>9631326
>>9631336

>>9631271
2^-17

>>9631349
>>9631336
mixing signals

>>9631271
1/131072 ?

I feel like my answer to this was valid and my attempt was unfairly marked as incorrect.

I suppose an argument could be made that I ought to have provided the simplest possible answer, and if the question had been "what is the shortest series of commands...", I would understand. But the question was "What commands would you issue...". When I imagine an equilateral triangle, I imagine one "sitting" on its base, not one "pointing" to the right.

>>9631357
>>9631349
>>9631336
>>9631326

>>9631359
It's not even high school math you fucking brainlet

>>9631358
but it even has a remark:
>assuming it starts at the center xOy and going north

it's a condition of the task, you CANNOT disregard it.

>>9631345
There are (100.000-16)*2^99.983 arrangements of 17 losses in a row among the 2^100.000 outcomes. Oh wait, I guess I'm double counting lots of them since an 18 loss streak would be counted twice, a 19 loss streak would be counted thrice, etc. Oh well, dunno if it can be salvaged.

>>9631367
point was there is liek 4 different answer dumbfuck

>>9631348
>>9631336
>>9631357
>>9631359
>1/131072

>>9631369
>>9631371
make it 5

>>9631358
T is a turn clockwise, it should be T60, T60 and T60 since it's a equilateral triangle.
Your solution assumes the robot is facing east at the start and that T goes counter-clockwise, in short a total fuckfest.

>>9631374
You're just calculating the chance of getting 17 heads in a row without considering the fact that we're throwing 100.000 coins.

>>9631249
Okay thanks anon. It seems like I end up amending my gaps (on a small scale) when it becomes obvious that they are a problem (i.e. reviewing trig basics during calc II) . But I don't wanted to be limited by them so I will still go over this book but probably a lot more liberally then I was planning.

>Only thing I would say is pay attention to developing your geometric intuition

I definitely will, thanks.

>>9631368
I interpreted "goes north initially" as meaning that the robot's initial orientation was north, and from that decided that I should correct its starting orientation to the one I wanted before drawing the first side.

I suppose that, since it does say "goes" north rather than "points" north, that does mean that the first side of the triangle should be parallel with the y-axis. Thanks

>>9631385
No, my solution assumes that the robot is facing north (but I want it to be facing 30deg clockwise from that), and that T goes clockwise. Notice that the provided correct solution also uses T120. My solution is the same except I changed the starting orientation when I shouldn't have.

>>9631387
Cant you read ?
>Toss a coin 100.000 times

>>9631336
>>9631374
Different anon here, I know absolutely nothing about statistics, but will be taking Statistic and probability courses in the future. I've heard from people that they just memorized a bunch of formulas in their stats courses, there is a way to learn statistic concepts intuitively right? Or at least find a way to derive these equations? I can't imagine doing well in a math course that I don't understand.

>>9631385
>>9631394
You both are incorrect.

it's an equilateral triangle, all angles INSIDE triangle must be 60 degrees , and since he is rotating CLOCKWISE respectfully to his current rotation (in relation to global axis/orthobasis) the turns has to be this way

>>9631298
but if av+w is in the subset, then 0 is since 0=(-1)v+v

>>9631406
Pic related is what I did. Robot starts at A, facing up. Turns 30 degrees, proceeds along c. Rotates 60+60=120 degrees at B, proceeds along a. Another 120deg at C, proceeds along b. All rotations are clockwise.

The intended/correct solution is exactly the same, except without the initial 30deg rotation.

>>9631387
>>9631401
So what's the correct answer ?
>50/50 Chance
>100.000 flips
>17 heads in a row

>>9631430
>The intended/correct solution is exactly the same
No it is not, it is more optimal - one less move

But it is similar, yes.

Again, we are back to: cannot disregard the condition.

>>9631397
Can't you read ?
> Calculate the chance of flipping 17 heads and 0 tail
The event of getting 17 heads in a row out of 100.000 flips does not require 0 tails. It includes anything from 0 to 99983 tails.

>>9631435
Dunno, I can't figure out how to count 17 heads in a row events without duplicates. I might make a program in octave to check what the probability should be.

>>9631416
Agreed, but it's an extra step. So your two step proof or the one step proof are both fine.

>>9631435
After running my short Octave script three times I got 16 heads in a row, 17 heads in a row and 14 heads in a row. I'm running it a hundred times now but it's surprisingly heavy. NB. I'm no programmer, no need to comment on efficiency.
d=0;
for j=1:100
a=[];
b=0;
c=0;
C=0;
for i=1:100000
b=round(rand());
a=[a,b];
if b>0
c++;
if c>C
C=c;
endif
else
c=0;
endif
endfor
if C>16
d++
endif
endfor

So, a coil is positioned so that its magnetic moment is antiparallel to a magnetic field. It then is rotated 180 degress so that the magnetic moment is now parallel to the magnetic field.
I'm being asked to find the change in potential energy. (U = - u x B)
But since they're both parallel to the field, wouldn't the change be 0?
However it says I'm wrong.

>>9630029
>how can I prove that √n is not bounded
just use the definition of what it means to tend to infinity
for the second thing i cant think of a nice proof, but using the binomial theorem is probably your best bet

>>9631487
yeah youre right. thanks

>>9631516
Out of 100 iterations 30 got 17+ streaks of heads.

Trying to make proofs of different basic Fourier Transforms, but am running into a problem with the constant function.
The way my professor did it in class was by taking the limit of the two-sided real decaying exponential. I got the same answer he did, but I feel like I did a bunch of handwaving when the frequency is zero.
Is there a better/more rigorous way of solving this one? My proof is in the pic

Can someone help me understand the meaning of this:

[math] \sum_{\text{all i}} | i \rangle \langle i | [/math]

I know that it equals the identity matrix, but I can't understand what the bra and the ket symbols mean when put alongside like that.

How come magnetic monopole's don't exist?

>>9631762
Let
P := |v><v|
act on a vector (ket) |w> as follows
P|w> = |v><v|w>
here c:=<v|w> is a scalar, so P|w> is a multiple of |v>.

Compare this with a vector [2,2] in R^2 and consider e.g.
P = [2,3] [2,3]^T
Then
P [7,4] = [2,3] * ([2,3]^T [7,4]) = 26 * [2,3]

So |a><b| is always a projection of vectors onto |a>.

If, like in your case, you take orthogonal projections and sum them all up, well, then you just end up with the identity.

>>9631762
ugh, that would take too long to explain. For the time being think of kets (>) as normal column vectors, and think of bras (<) as row vectors.

Compare this with a vector [2,3] in R^2

>>9631762
it is an operator. When you operate it on kets [math]|k\rangle[/math], you get [math]\langle i|k\rangle[/math] terms which is equal to [math]\delta_{ik}[/math]. In particular, every term in the sum gets eliminated except the [math]|k\rangle\langle k|[/math], but operating it on [math]|k\rangle[/math] gives [math]|k\rangle[/math] again. So you see that "operating" that sum on a ket gives you another ket, and since the result after applying the operator is the same ket, then you can identify this operator with the identity operator.

>>9622645
Is there any way to emotionless other than clinical depression? How do I stop feeling things?

>>9631792
Wow, thanks! That makes a lot of sense now.

How do you prove [math] cot^2 x + csc^2 x = cot^2 * csc^2 [/math] ?

>>9632255
[math] cot^2 x+csc^2 x=cot^2 x ∗ csc^2 x [/math]
*
Sorry.

>>9632255
>>9632264
that's not true though
https://www.wolframalpha.com/input/?i=cot%5E2(pi%2F4)%2Bcsc%5E2(pi%2F4)+%3D+cot%5E2(pi%2F4)*csc%5E2(pi%2F4)

What field of physics is for lazyasses? i have the grades and intelligence to get into almost any program but im also a lazyass. i hear optics is pretty laid back

>>9632287
Thanks a lot, I thought something was wrong.

>>9623323
What can I do with that? aren't we talking about integrals? if a trigonometric integral shows up I would use Simpson method honestly, fucking trigonometric integrals are pure bullshit.

Alright folks, I was raised in a shitty town with a family that believed that we were born genetically inferior when it comes to math. I was never pushed to excel in math because, “well I did bad at math in college it’s just genetics”. Now, I’m in Calc 2 in Uni and I’ve started to realize that when I try in math, I’m not retarded. I actually sort of enjoy it, a lot. I really want to do very well in math and continue it in college. Do you guys have any resource recommendations?

Can I finish the whole high school math and cover the basics of calculus in 4 months? I am currently doing Lang's Basic Mathematics and James Stewart's Algebra and Trigonometey.

I quitted school at 6th grade and I am just returning to college thanks to the government's special exam.

>>9633031
>Can I finish the whole high school math and cover the basics of calculus in 4 months?
You won't know unless you try.

>>9633031
Yes, easily.

>>9633031
>in 4 months
depends on your genetics blessing towards math

>>9622645
I though a/b/c = a/bc but with this we have (a/(b/c))*(b/c) = a/bc * b/c = a/c * 1/c = a / c^2 but we should have the result "a", please tell me where I'm wrong.

>>9633156
Does not like you are wrong anywhere, what the original question?

>>9633156
>I though a/b/c = a/bc
PLEASE use brackets, or use LaTeX to make clear what you mean.

[math]\frac{a}{\frac{b}{c}} = \frac{a \cdot c}{b} = c\frac{a}{b}\neq \frac{a}{b \cdot c}[/math]

>>9633170
The question is what is a source of the error, because (a/(b/c))*(b/c) = a (I divide then multiply a by the same thing (b/c), but in simplifying (a/(b/c)) by a/bc I find (a/(b/c))*(b/c) = a / c^2, so there is a problem here.

>>9633173
but you are wrong

[math]
\frac{a}{b} : c = \frac{a}{b} * \frac{1}{c}
[/math]
where did you get ca/b?

>>9633173
oh, so a/b/c isn't the same thing that a/(b/c)?

I believed a/b/c/d = (a/b) / (d/c) so
a/b/c = a/b/c/1 = (a/b) / (1/c) = (a/bc)

>>9633193
not him but ofc it is not the same thing.

a/b/c is basically a : b : c

since it is division everywhere, we use left-to-right order so we can write it as
[math]
\frac{a}{b} : \frac{c}{1}
[/math]

>>9633191
>but you are wrong
Am I?
For clarity this is what mathematicians mean:
[math]c\frac{a}{b} = c \cdot \frac{a}{b}[/math]

I even asked MATLAB, but it agreed with what I wrote.

>>9633193
>oh, so a/b/c isn't the same thing that a/(b/c)?
They are not the same, that is why brackets are extremely important.

>>9633203
>Am I?
Yes, see >>9633196

If no brackets specified then order is linear, left-to-right:
> a/b/c is basically a : b : c
So we divide a by b and then divide result by c

>>9633211
wow I fucked it up big time let me rewrite

10/5/3 = 2/3
[math]
\frac{10}{5} : \frac{3}{1} = \frac{10}{5} : \frac{1}{3} = \frac{10}{15} = \frac{2}{3}
[/math]

>>9633206
>Yes
>> logical(((a*c)/b)==c*(a/b))
Returns 1.
>> logical((a/(b/c))==((a*c)/b))
Also Returns 1.

Please be aware that the first fraction I use is (a)/(b/c), this is made clear by the size of the lower part of the fraction.

>>9633211
For the love of god PLEASE start to use brackets.
Do you mean 10/(5/3) or (10/5)/3?

>>9633196
Ok thanks, I think I got it.
If I got it so this following operation (quite unpleasing sorry) is right and we can't simplify more right?
a/b/c/(d/e)/f/g/h/(i/j/k)/l
(a/b) *((d/e)/c)*(g/f)*((i/j/k)/h)*(1/l)
(ag/bfl) * ((d/e)/c) * ((i/jk)/h)

>>9633218
>For the love of god PLEASE start to use brackets.
You DONT need to use brackets if it is the same binary action everywhere, the order of execution exist for this and unnecessary brackets lower readability.

You (well, not you clearly) don't need bracket to be able to read:
a:b:c
because you know you divide them one by one, to the right.

However, when you NEED to specify order only THEN you use brackets:

a/(b/c)

Example:
10/5/3 = 2/3 = 0.666666666666666666
but
10/(5/3) = 5.999999999999999

>>9633235
>You DONT need
Yes, you don't NEED, but you ALWAYS should.

>You (well, not you clearly)
Exactly, that is why in my first post I asked to put brackets.

>a:b:c
":" is not used for division anywhere in serious mathematics.

>5.999999999999999
Please never use the that calculator again.

Is it viable to get a degree in chemical engineering?

>>9633232
No you can use linear transformations for
>a/b/c/(d/e)/f/g/h/(i/j/k)/l
since you can write them as fractions:
https://www.wolframalpha.com/input/?i=a%2Fb%2Fc%2F(d%2Fe)%2Ff%2Fg%2Fh%2F(i%2Fj%2Fk)%2Fl

>>9633247
stop acting retarded after being told

>>9633253
>stop acting retarded after being told
Told what?
Nothing I said was ever wrong, I just asked for brackets, as it is common everywhere in mathematics.

>>9633258
No they arent. Nobody uses them because of OCD, they are used when they are necessary,

>>9633262
Nobody writes things like a/b/c in serious mathematics

>>9633439
Sometimes when you simplify things you do

>>9633624
You don't. You'd use LaTeX/proper fractional notation.

>>9633675
No, very often you'd like to write it as
[math]
a : b : c
[/math]

if a,b,c are already fractions (or fractions of fractions or polynomial fractions) and you just want a simple look at a glance

>>9633439
>Nobody writes things like a/b/c in serious mathematics
I do.

>>9632827
>believing mathematic abilities depend on genes
Kind of stupid logic, no offence.
>Resources
Just fucking sit down and do shit, first with books, then without them. The one and only resource you need is time.

>>9627246
motherfucking ms fcs

>>9633235
> You DONT need to use brackets if it is the same binary action everywhere, the order of execution exist for this and unnecessary brackets lower readability.
Except that the OP's entire problem revolved around misunderstanding the associativity:
(a/b)/c =/= a/(b/c).
Every known convention has / associate to the left, but that is irrelevant if you're communicating with someone who might not know that, and even more irrelevant if you're communicating with someone who has actually demonstrated that they don't know that.

Note that not all infix operators are conventionally left-associative. Exponentiation is normally right-associative, i.e. a^b^c = a^(b^c).