/sci/ - Science & Math

>have to take all these pre-requisites before getting to my major's requirements
How am I supposed to do this before age 40?

>>11094658
>How am I supposed to do this before age 40?
What have you tried?

>>11094658
>Not starting at analysis.
Kek.

>>11094680
im taking basic algebra currently

>>11094658
>>11094686
Please don't post here until you've finished your bachelors and a masters degree.

>>11094698
t. no PhD

what do these buttons do

>>11094565
My friends, operation math ethnostate is a go.
We plan to build a math monastery by pooling money together to get a temple of some sort.

Only join if you aren't shit at math. I mean like 3 Phds minimum.

https://discord.gg/AuSqAx

almost done. just 7 sections to go

Would my feeble hs mind be able to handle Analysis and Algebra? I have experience with proofs, but very minimal in calculus.

>>11095103
Yes. I sucked ass at calculus. Turns out I was just to smart for calculus, and analysis went much smoother

>>11095112
>To

>>11094887
>mathnostate
How did you miss this

>>11095103
>Would my feeble hs mind be able to handle Analysis and Algebra?
Why don't you try them and find out?

>>11094681
this

>>11095236
kek

>>11095250
i'm not kidding though, calc is pointless to a mathematician, i don't want to compute shit, i just care about the theory.

Have fun bros.

>>11094658
>How am I supposed to do this before age 40?
Start at 6 years old like every other person.

>>11094779
The things they do on pretty much every other calculator.

>>11095308
I'm looking at all these problems and don't see any that would bring some benefit after solving them. You would just waste your time for nothing. The absolute state of olympiad mathematics

>>11094658
skip history
also
>matrix analysys
>concepts of geometry
>not starting with calculus immediately

>>11095300
>calc is pointless to a mathematician
this is a big problem with mathematicians nowadays, they go off into abstraction and don't have a solid foundation in the dirty work, so they end up drifting further away into meaningless shit and abstraction for the sake of abstraction
It's exactly the same shit everyone hates category theorists for except nobody admits this is even a problem aside from the occasional Von Neumann quote or something

Why the fuck did you make the new before he bump limit.

>>11095756

Since there's no actual math being discussed...
*opens book to random page*

(a) Given two conics in different planes of the affine space [math]\mathbb{R}^{3}[/math], with two common points, and given a point not contained in these planes, prove that there is a unique quadric containing the conics and the point.
(b) Find the quadric containing the point [math](1,1,1)[/math] and the circles [math]x_{1}^{2}+x_{3}^{2}=1[/math], [math]x_{2}=0[/math] and [math]x_{2}^{2}+x_{3}^{2}=1[/math], [math]x_{1}=0[/math]. Find a quadric containing the circle [math](x_{1}-1)^{2}+x_{3}^{2}=1[/math], [math]x_{2}=0[/math], the parabola [math]x_{2}=x_{3}^{2}[/math], [math]x_{1}=0[/math] and the point [math](1,1,1)[/math] (see pic.) .

>>11095963
>see pic
here.

*opens book to random page*

Prove that if [math](f_{1},f_{2})[/math] is a random vector whose density of distribution is [math]q_{(f_{1},f_{2})} : \mathbb{R}^{2}\to\mathbb{R}[/math] , then the density of the distribution of [math]f_{1}-f_{2}[/math] is [math]q_{f_{1}-f_{2}} : \mathbb{R}\to\mathbb{R}[/math], where [math]\displaystyle q_{f_{1}-f_{2}}(x) = \int_{\mathbb{R}} q_{(f_{1},f_{2})}(x+y,y)dy[/math] , [math]x\in\mathbb{R}[/math].

Last one
*opens book to a random page*

Let [math]R[/math] be a ring, not necessarily commutative, and let [math]M[/math] be a left-[math]R[/math]-module. Prove that [math]M^{\lor}[/math] carries a natural right-[math]R[/math]-module structure. Prove that [math]R^{\lor}[/math] is isomorphic as a ring to the opposite ring [math]R^{\circ}[/math]

>>11096004
trivial

Bonus round:

Let [math]A\in M_{m,n}(\mathbb{F})[/math] and let [math]B\in M_{m+n,m+n}(\mathbb{F})[/math] be the square matrix [math]B = \begin{bmatrix} 0 & A \\ A^{*} & 0 \end{bmatrix}_{\text{block}} [/math]. Show that, counting multiplicity, the nonzero eigenvalues of [math]B[/math] are precisely the singular values of [math]A[/math] together with their negatives.

>>11095709
It's hardly a big problem, it just depends what kind of math you're doing. Not everybody does combinatorics or hard analysis.

>>11096011
Ignore him. He's just posting words, in that he has no idea the meaning of the things he posts.

>NOOO DON'T POST ACTUAL MATH WE NEED TO TALK DRAMA ABOUT CATEGORY THEORISTS ON TWITTER FOR 200 POSTS!!!

Any more books like Nahin's Inside Interesting Integrals?

>NOOO DON'T POST DRAMA ABOUT CATEGORY THEORISTS ON TWITTER WE NEED TO TALK ACTUAL MATH FOR 200 POSTS!!!

>>11095147
we building a mathnostate indeed

plz, only high iq faggots. No category theorists!
https://discord.gg/AuSqAx

>>11096075
you have no future in mathematics

>>11094686
this should be grounds for underaged and b&

>>11096026
What is [math]\mathbb F[/math] ?

>>11096409
a field

pretty sure this thread, this board in particular has been irrevocably flooded by high schoolers and first year undergrads. they were always here before but not in the droves they are now. i blame msm for putting 4chan in the spotlight.

>>11096721
Sure but what field ? What is * if F is arbitrary

>>11096728
either [math]\mathbb{R}[/math] or [math]\mathbb{C}[/math]

>>11096737
Or the p-adic fields, or any of the number fields, or any finite field, or anything else.

Some elaborations on EFQ (ex falso quodlibet, principle of explosion)

https://youtu.be/eeLa9tIhFMs

>>11096764
it's either reals or complex, but be my guest, go ahead and try it for other fields to see what happens.

>>11094779
t. underaged zoomer

>>11095709
Oh, believe me, they make us do the dirty work, real analysis in particular, the theory is even uglier than the computations in the 'practical' problems, i mean did you see the proof of the implicit function theorem for example?
Alsa, there is a quote, that goes something like:"A mathematician is the guy who thinks for 2 hours to save himself from a 10 minute calculation", it's something to live by.

Suggest me some algebra books to self-study proofs.

Why can't I imagine tangent vectors of a manifold that's not embedded in a higher euclidean space?

>>11096737
Alright, well by the Schur complement formula yields:
[eqn]\begin{vmatrix} XI_m & A \\ A^* & XI_n \end{vmatrix} = X^m \det(XI_n - X^{-1}A^* A) = X^{m-n}\det(X^2 - A^*A)[/eqn]
which gives the desired statement

>>11096026
Let [math] n [/math] be an odd integer [math] >2 [/math] and let [math] f(x)\in \mathbb{Q}[x] [/math] be an irreducible polynomial of degree [math] n [/math] such that the Galois group [math] Gal(f/\mathbb{Q}) [/math] is isomorphic to the dihedral group [math] D_n [/math] of order [math] 2n [/math]. Let [math] \alpha [/math] be a real root of [math] f(x) [/math]. Prove [math] \alpha [/math] can be expressed by real radicals if and only if every prime divisor of [math] n [/math] is a Fermat prime.

>>11095756
>Why the fuck did you make the new before he bump limit.
What do you mean?

Threadly reminder to work with physicists.

>>11097065
Did you ever figure out what this means?

>>11097120
>Did you ever figure out what this means?
What do you mean?

>>11097123
How does the image support working with physicists?

>>11097127
>How does the image support working with physicists?
Which part do you not understand?

What are we learning today fags, I'm supposed to have a grasp on Casson-Gordon invariants by the end of the semester

Also what're your departments like, mine is mostly redditors who have a penchant for analysis and complex geometry and normies who do algebra

Is the set of sequences {0,1}^N in L-infty (the dual of L_1) under the weak star topology open?

How can I see this?

>>11097136
Am I just being shitposted with? I was asking an honest question, which wasn't answered last time I checked about a month ago.
The image depicts confusion on both sides when they switch, so neither the first pair nor second pair of images show superiority/inferiority of either party.
So the "part" I don't understand is the statement itself in relation to the accompanying image.

>>11097237
sorry, I meant does it have any open subsets?

>>11097260
Yukarie poster did actually answer that the last time.
The picture bascially shows how some of the big results in math and physics respectively became later important for the other field (results and tools from algebraic topology becoming very useful in tqft and condensed matter, toosl from (q)ft becoming useful in geometry) and working together is thus beneficial for both groups.
The picture is taken from "Quantum fields and Strings" by Deligne et al, so try reading that if you are still curious.

>>11097195
>fags
Why the homophobia?

>>11096817
>>11096817
Because you haven't learned about the exponential map yet.
>>11096004
I always find it weird when a book asks me to prove there is a natural structure on something.
Shouldn't it just ask me to construct a natural structure?
>>11097062
Thread was made circa 305 posts.

What should I learn next?

>>11097863
>I always find it weird when a book asks me to prove there is a natural structure on something.
>Shouldn't it just ask me to construct a natural structure
Same thing.

>>11097883
seems like you've covered fields, linear algebra and linear programming, polynomial rings, unique factorization domains, integral domains and their fields of fractions, quotients of polynomial rings by ideals and radical ideals in general, quadratic forms and multilinear algebra, basic lie theory and the exponential map, and introductory classical algebraic geometry and arithmetic geometry. seems like there's also some composition series and elementary number theory in that last chapter.

you seem to be lacking analysis. i recommend the stein & shakarchi series.

>>11097195
Still working on the same thing as last week, namely using equivariant (twisted) [math]K[/math]-theory to classify LSM theorems and topological crystalline orders. Also I've been reading up on developments in Baum-Connes and the assembly map in order to understand what's going on on the operator [math]K[/math]-theory side as well, since this will help with constructing explicit models.

How does one stop oneself getting dragged into the /pol/ tier threads when coming to /sci/ to explore different perspectives on maths?
Could someone recommend a good primer on stats it seems to be a topic I'm lacking in.

>>11097195
>What are we learning today fags
Recapping the Eilenberg-Moore SS.
>Also what're your departments like, mine is mostly redditors who have a penchant for analysis and complex geometry and normies who do algebra
At least on the postgrad & research level it is very nice and fun. The undergrads may be redditor tier scum, but us big boys (and one big girl) are high quality personnel.

>>11097195
Basic measure theory. I find it really interesting

>>11097195
>What are we learning today fags,
spin geometry. started two days ago.

>Also what're your departments like
analysts do ODE, something semi-periodic something. a few people do CR-geometry.
normie algebraists do mostly semigroups.
a SHIT-TON of based algebraists do category theory. seriously though, my uni is a fucking lair of undergrad category theorists.
geometers do parabolic geometries.

>>11098553
>and one big girl
a big girl(male)?

>>11098553
girls can't into math lol

I have no friends and I am stuck, I am so so sorry.

Is lim x-> inf (1-A^{B*log(x)})^(C*x) = 0 or not?

A is a constant between 0 and 1, B is a positive integer, C is a positive integer.

I'll repay in UGO JESSES

>>11099162

>>11099167

>>11099162

Preface: in airport tired af

B is a positive integer so 1>=. Any value, our exponent will tend to infinity.

Hell, I'm going to say the limit is 1. Anyone wanna disagree feel free, I'm just going off of purely feel atm.

>>11099192
I appreciate your input.

>>11099209

As for reasoning I'm thinking the A^B term will tend to 0 which will make the statement just 1^x which we can consider 1.

>>11096723
Why would msm put our basket weaving website in the spotlight?

>>11099162
All right, first, note that [math]A^{B\log x} = x^{B\log A}[/math] (not very important, but I want to keep it like this).
Now, note that [math]\log(1-x^{B\log A})^{Cx} = Cx\log(1-x^{B\log A})[/math]
Since [math]0 < A < 1[/math], we know that [math]x^{B\log A}[/math] goes to 0 as [math]x[/math] goes to infinity.
Apply Taylor's formula to get [math]Cx\log(1-x^{B\log A}) = -Cx\left(x^{B\log A} + O(x^{2B\log A}))\right) = -Cx^{1+B\log A} + O(x^{1+2B\log A})[/math]
Now there are three cases:
.If [math]1+B\log A > 0[/math], then because C is positive this sum goes to [math]-\infty[/math] as [math]x[/math] goes to infinity, and therefore, passing to the exponential, [math](1-x^{B\log A})^{Cx}\underset{x \to \infty}{\to} 0[/math].
.If [math]1+B\log A = 0[/math], then this whole sum is equal to [math]-C + O(x^{-1})[/math] and converges to [math]-C[/math] as x goes to infinity, and thus [math](1-x^{B\log A})^{Cx}\underset{x \to +\infty}{\to} e^{-C}[/math]
.If [math]1+B\log A < 0[/math], then the sum converges to 0 as x goes to infinity and therefore [math](1-x^{B\log A})^{Cx} \underset{x \to \infty}{\to} 1[/math]

You. Construct the reals. Now.

>>11099314
Assume they exist. Done.

>>11096026
this is so fucking easy that you should embarrassed to have asked the question.

did you register on lgbtmath.org anon? are you not an ally?

>>11099314
Something something equivalence classes of Cauchy sequences.

>>11099551
>are you not an ally?
No, if anything I am an axis.

Can someone give me an example where the language of schemes is the RIGHT way to look at a problem in algebraic geometry or number theory, the statement of which doesn't involve the notion of schemes itself. Why can't you use varieties to solve it?

Analysis seems to be easier and more straight forward than linear Algebra. Thoughts?

>>11099608
you may just have a mind for it but the majority of people would tell you you're wrong

>>11099608
agreed. Linear algebra is more bigger picture stuff whereas i feel analysis goes deep in the nitty gritty.
Always was better at analysis until I took topology, that rekt me.

>>11099608

Nope. Analysis is full of inequalities which are harder than the equational reasoning typical of algebra.

>>11099608
>Thoughts?
Meaningless comparison.

>>11099608
you’re low iq

>>11099764
why would he be when analysis is considered harder than linear algebra?
Me thinks you're low iq

>>11099596
Alggeotards got memed on by Grothendieck and now just pretend schemes are useful to appear smart

I was suggested an assistant prof. position in AI standardization. Do anyone here have any experience with standardization? Feels like I'd bury my applied maths background switching to such a position. Been google scholaring the topics and haven't found anything even remotely "mathematical". The perspective of ending this god damn PD fuckery is attractive as hell though.

>>11099895
Appraisal had nothing to do with his impressions of the relative difficulty of either class.
>methinks
you should kill yourself

>>11094565
Whats up?

Im a senior EE student.

Next trimestre im starting a math diplomate, for the math diplomate im going to take analisis 1 thru 3 and multivariable data analysis. If I have time ill take a few more classes, namely DEs for mathematics, PDEs for mathematics and maybe numerical calculus.

What can I expect? Any pointers?

>>11097262
what is the weak star topology?

I've been playing this puzzle game called Transmission on my phone (free on Android).
Can such puzzles be expressed and solved mathematically?

>>11100442
>Can such puzzles be expressed and solved mathematically?
What have you tried?

>>11099639
>more bigger picture stuff

>>11100451
I have no idea where to even start because of the game's mechanics. I could try to explain them here but I think it would be less confusing if you tried playing the game yourself.

*reflects on years of mathoverflow posts that resulted in no publications*

>>11100546
what the fuck was his problem?

>>11099608
Linear algebra is literally THE easiest subject in maths. Dunno what you're talking about.

>>11099608
>>11100561
he's talking about first semester linear algebra vs first semester calculus course. there's no way this was written by someone who knows at least something about real math, I mean come on.

>>11100190
Anyone senpai?

>>11097195
I'm suffering through statistics.
Once that clears up it's back into nonlinear regularization.
>>11098553
>recapping Eilenberg-Moore SS
Fuck, I need to recap that too.
I need to recap a lot of algebraic topology.
Thanks for reminding me.

>>11100826
>suffering through statistics
lol are you legitimately retarded? probability and statistics is by far the easiest math course. i literally don't study at all, never show up to class, and finish every test in half an hour and get 100s on them

>>11099551
Yep, already on the mailing list.
>>11100826
>nonlinear regularization
Tell me more.

help gamers what does the group "P({1, 2}) with symmetric difference" mean

>>11099582
abscissa niggas be like

>>11094565
yo yo yo
anyone here interested in making an irl math monastery? if so join this server:
https://discord.gg/F3YT9mW

>>11101111
>help gamers what does the group "P({1, 2}) with symmetric difference" mean
P({1,2}) = power set of {1,2}

>>11098502
start killing yourself

>>11100309
topology of pointwise convergence for linear functionals.
i.e., here a subbase of open sets is given by sets of the form {g in l^infty : |g(v) - f(v)| < epsilon} for fixed f in l^infty, v in l^1, and epsilon>0.
I doubt it has an open set, haven't really thought about it. weak* is fucky though.

>>11101230
Careful. The weak topology is the weakest topology on which the linear functionals are continuous. For linear [math]operators[/math] on a Banach, being continuous is equivalent to being bounded, but this may not be true once you take away the "Banach" qualifier.
In addition, weak-* topologies also have to respect the involutive [math]*[/math]-structure.

>>11101262
i hadn't thought about the difference between the topology on functionals and operators, but these are operators on l^1, so it should be fine.
i'm just assuming the topology respects the *, i don't want to think about such things.
in any case, it's pretty obvious the set has empty interior.

>>11101298
>>11101262
no wait you've confused me again. these are totally linear functionals. we're not multiplying, we're multiplying then integrating (we're talking about the dual). fuck off, i was right about this particular scenario and don't need the irrelevant commentary.

>>11101310
?
My commentary definitely applies for general commentary on what a weak-* topology is, which is presumably what you replied to. Not sure why you're so defensive, I'm not here to condescend to nor patronize you.

>>11099596
(You)

>>11099608
>linear
>not the most straight forward

>>11098502
>How does one stop oneself getting dragged into the /pol/ tier threads when coming to /sci/ to explore different perspectives on maths?
Never visit /sci/ outside of /mg/, it is full of conspiracy theorists, from schizo flat earthers to IQ deniers and racial egalitarians.

>>11099551
Is there any actual content and/or cybernetically enhanced xenomorphic post-binary gender accelerationism, or is it just "hey this tranny got full marks, women proven to be smarter than men!"?

>>11101626
Nope, you get notifs about LGBTQ+ events/conferences. That's about it really.

>>11101319
of course it does, but i was just stating what the topology on l^infty was.
>i'm not here to condescend to nor patronize you
prefacing your post with "careful" seems to indicate that you found an issue with my post. i simply wanted to clarify for the dude that asked that what i told him was perfectly correct.

>>11100546
>many_such_cases.m

>>11101079
>by far the easiest math course
Nope, that would be algebra.

>>11101319
>I'm not here to condescend to nor patronize you.
You definitely have autism if that is the case.

>>11099596
>any problem involving intersections and multiplicities. If you do not allow nilpotent elements in rings of functions (ie. work with varieties), then you can not see intersection multiplicities
A prototypical example of this is the moving lemma, and as an application, Bezout's theorem, the statement of neither of which involves schemes.
>any problem involving "families" of varieties, moduli problems, deformations etc.
In many cases, the existence of moduli spaces for algebraic objects is not done by finding explicit charts, but rather using complicated existence theorems (GIT, Artin algebraization, etc.) that use the full strength of scheme theory.
An example of this is the construction of the Hilbert scheme of a projective variety: The space parameterizing all closed subschemes of a variety.

>>11099596
>>11101973
(cont.)
>many problems involving varieties over non-algebraically closed fields, especially imperfect fields.
This is more of a general principle: it is often very useful to look at the solutions of a system of equations over a field in extensions of that field or more generally algebras over that field.
If you want to solve a problem over a non-algebraically closed field, a basic idea is to extend to the algebraic closure, solve the analogous problem, and see if you can transfer the result to your original field.
This method is called base change + descent. Sometimes, descent is easy and does not require scheme theory (for example, you don't need scheme theory to prove that two real matrices that are similar over C are similar over R: exercise), but sometimes you do need something stronger, like faithfully flat descent, to prove that a property over [math]\bar k[/math] descends to k.
For that reason, people try as hard as possible to make constructions that are preserved by base change and faithfully flat descent.
For example, it has led algebraic group theorists to adapt group-theoretic concepts (normalizers, centralizers, kernels, etc.) to make them invariant under base change and descent. It makes them harder to compute, but very useful for proofs.
Algebraic group theorists use this "base change and descent" very often. An example of this is the classification of linear algebraic groups over an arbitrary field (still in progress). It relies heavily on the results over an algebraically closed field (achieved by Chevalley, Borel, Tits etc.) and scheme theory.

>>11101982
Not the guy you respond to, but thx.

I like groups over finite field extension over Q, I might need to look into more modern algebraic geometry (or maybe not).

>>11095308
problem 4 smells like basic stat mech

Can someone draw me a picture how does a metric space (X,d) where d:X times X -> R_>=0, forall x,y in X x != y then d(x,y) = 1, if x = y then d(x,y) = 0 look like?

>>11102235
That's just a graph where d functions as a predicate telling you if two vertices are different. If you want an isometric embedding, think of the pyramid with 4 triangular surfaces in R^3

>>11102235
For X finite, it is what is called a simplex.
For 3 points, you get the vertices of an equilateral triangle, for 4 the vertices of a regular tetrahedron as >>11102293 said
For |X| > 4, you cannot realize it in 3D, but it will be analogous to these examples.

>>11102293
>>11102313
thanks dudes, did you realize that all by yourself or did you read it somewhere? if the latter then I'd need a source since the book must be high quality

>>11102313
>>11102355
It's not a simplex since the filling isn't part of it

>>11101142
nah, it will get filled with horny troons that will ruin the experience for everyone else.

>>11101626
implying that g/acc isn't just tranny mental wankery to pretend they're intellectuals, back off nyxland, this place isn't for you.

I am reading this article, and it starts with this:

> Let [math]C[/math] be a smooth quartic in the (complex projective) plane.
> Let [math]l[/math] be a line transverse to [math]C[/math] with 4 distinct points of intersection.
> The double cover [math]C_l[/math] of the line branched above these four points is a smooth curve of genus one.

In this case, what is the double cover [math]C_l[/math] meant to be?

For example, if I consider the curve [math]X^4+Y^4+Z^4=0[/math] and the line [math]X=0[/math], the intersect in the four points [math][0:e^{in\pi /4}:1][/math] for [math]n=\pm1,\pm 3[/math].

>>11102456
Yes, should have said the vertices of a simplex. That is what I said afterwards

>it doesn't work
>check it again
>see mistake
>fix mistake
>it still doesn't work
>tfw

>>11102545
>problems of people who don't know logic

>>11102495
Here are some ideas:
A double cover of C is the same as a field extension [math]k(C) \simeq k(t) \hookrightarrow K[/math] of degree 2.
Assuming k has characteristic not 2, we may write [math]K = k(t, \sqrt{f(t)})[/math], with [math]f[/math] a separable polynomial.
This field is the field of functions of the curve with affine equation [math]u^2 = f(t)[/math].
This cover ramifies at every zero of [math]f[/math], and once more at the infinity point, hence it ramifies at four points iff f has degree 3, in which case it has genus 1.

>>11102557
Ugh, I meant to say a double cover of [math]l[/math], of course...

>>11102569
>>11102557
alright, thanks for clarification there was confused.

will look into it

>>11102557
would we take [math]f[/math] here to be the equation defining the curve?

>>11102862
I’m not sure what curve you mean (there is C, l and our double cover).
What I meant to say is that, if [math]C_l[/math] is a double cover ramified at four points, then [math]\mathbb C(C_l) = \mathbb C(t, \sqrt{f(t)})[/math].
To get f, you need only find some rational function on [math]\mathbb C_l[/math] that does not come from a function on [math]l[/math].
Then, it satisfies a degree 2 equation with nonzero discriminant. You may then take f to be the squarefree part of that discriminant.
And the last point is that you can take [math]\mathbb C_l[/math] to be the projective completion of the affine curve [math]u^2 = f(t)[/math]. So, in some sens, yes, it defines the curve, but it is not literally the equation of the curve.

>>11100550
lesswrong and starslatecodex

>>11102862
I’m not sure what curve you mean (there is [math]C, l[/math], and [math]C_l[/math]), so let me reformulate.
What I meant to say is that, if [math]C_l[/math] is a double cover of [math]l[/math], then [math]\mathbb C(C_l) = \mathbb C(t, \sqrt{f(t)})[/math].
To find an appropriate f, you need only find some rational function on [math]C_l[/math] that does not come from a function on [math]\mathbb l[/math] (ie. a function that is not constant on fibers).
Then, it satisfies an equation of degree 2, with coefficients that we may take in [math]\mathbb C[t][/math], that has a nonzero discriminant.
Then, you may take f to be the squarefree part of this discriminant.
The last point is that it follows from the above that [math]\mathbb C_l[/math] is isomorphic to the completion of the affine curve [math]\{u^2 = f(t)[/math].
So, in some sense, yes, f defines the curve [math]C_l[/math], but it is not exactly an equation for [math]C_l[/math].

>>11101892
Sorry for trying to facilitate sincere mathematical discussions.

>>11100550
Sex Therapist
>Drop PhD go SV Machine learning things, $500K for Sex Therapist

>>11102980
I point out that you have autism, because most of your posts read like pure show offs where you avoid saying anything about the Problem at hand and make some vague allusions to some very advanced topics which the person clearly has never heard about and has no ability to understand.
If you genuinely believe that your posts are not condescending or patronizing (or at least do not appear as such) you are autistic and I mean that word in it's actual meaning, meaning that you can not properly interpret social interactions.

Note that I am not alleging any ill intentions on your part, just that you seem entirely unaware of how people perceive your posts.

>>11102948
Could you give me a quick rundown on what the fuck they are and how they have anything to do with Yuan?

>>11103082
I have never done this aside facetiously in /sqt/ or threads where an extremely stupid question was asked, and even in those instances I make sure the questions were answered in a convoluted way.
I don't mean to make you feel insecure when I post but that's on you, not me. Work on yourself.

>>11103082
This.

>>11103089
>everyone who cringes at me spending 20 minutes copying the nearest textbook into TeX to try and impress undergrads on 4chan is just insecure

>>11103089
Even in response to perfectly reasonable questions, you very often answer at such an unnecessary level of generality that, if the asker had the background to decipher what you wrote, they definitely wouldn't be asking the question. God help anybody you might teach in person.

>>11103089
>I have never done this
That is false, it is very consistent behavior with you.
Just see your irrelevant commentary in >>11101262 as a not-all-that-offensive version of what I am pointing out.
Nobody wanted to hear your commentary on the weak topology or continuity of Operators being related to the Banachness of the space.

>I don't mean to make you feel insecure when I post but that's on you, not me. Work on yourself.
Since I am one of the approximately 5 people in this thread who actually has a degree in mathematics you aren't any more intimidating than the average PhD student, which I am afraid to say isn't really all that threatening to me.

I have to admit that sometimes I am tempted to do as you do and just mention something somewhat complex the person clearly either doesn't know or care about, so I kinda get where you coming from, but I also realize that isn't a good thing and most definitely isn't helpful.

>>11103122
>irrelevant
How is talking about the very definition of weak *-topology irrelevant to a question about weak *-topology? The Banachness of the space is crucial for characterizing what weak-continuity means. If you have a degree then you should know this.

>>11103135
>The Banachness of the space is crucial for characterizing what weak-continuity means.
And the question was about [math]L^{\infty}[/math], which is Banach, so even if give you the purest possible intentions you're still just being an obnoxious pedant correcting things that aren't wrong in the context they're stated.

>>11103135
>How is talking about the very definition of weak *-topology
You didn't do that.

Nobody who asks about the definition of the weak * topology is unaware of basic functional analysis, the person clearly did not want some commentary on basic functional analysis and a semi interesting fact about the weak topology.

If I ask "what is a weak derivative?" I neither am interested in hearing about the absolute continuity of the function in each component almost everywhere, nor about commentary on why partial differentiation is true in calculus.
Both are just irrelevant commentary, although clearly not unrelated.

>>11103082
Yukari tranny pseud blown the fuck out

>>11103167
>And the question was about
No. The question was >>11100309: "what is the weak star topology?", with zero reference to any Lebesgue space.
>>11103171
>absolute continuity of the function in each component almost everywhere
You should be though, especially the almost everywhere part, if the subject really doesn't know what a weak derivative is. Just writing out the defining formula doesn't say much.

>>11103182
>No. The question was >>11100309: "what is the weak star topology?", with zero reference to any Lebesgue space.
There is quite literally a reference to a particular space if you follow the reply chain up two posts.
I understand you're struggling to not appear like a faggot here, but surely you can do better than weaseling around like this.

>>11103104
Hahahaha

>>11103184
>if you follow the reply chain up two posts
I didn't and never intended to. When did this become the point of intention?

>>11103182
>You should be though
You can barely explain the ACM characterization in a single 4chan post, if you are replying to someone you also have to understand what they are asking for, either you both waste your time.

And yes, there are at least 4 ways of defining weak derivatives that I know of and each of the gives a different view on the issue, but if it comes to that, cite some book because it will take dozens of posts to explain.

>>11103188
>resorting to trolling to try and damage control
pathetic.

>>11103188
Interjecting into a conversation you didn't even follow to give some irrelevant commentary on something kinda related to something the other people talked about seems like autistic behavior.

>>11103194
What?
>>11103199
Ok, whatever you say.

As a observer, it's hilarious that some people actually consider yukariposter to be a genius. I haven't seem them solve one actual problem in any of these threads. Just throwing buzzwords and citing irrelevant facts.

Hey guys, I'm a complete brainlet when it comes to math. And by brainlet, I mean I'm a highly paid computer science graduate who doesn't remember any math. How do I get into useful math? Right now I'm going through http://www.jerrydallal.com/LHSP/LHSP.htm.. Any suggestions? I work with cryptography and data pretty often

I want to do a masters so I feel like I should be better at maf

Damn, the Touhou MathPhys poster really got btfo. He seems like a cool guy, but I agree he has a habit of vomiting out complicated things that can give the effect of making him seem super knowledgeable, despite not contributing to the conversation in a meaningful fashion.
We get it, you're knowledgeable about your field of study. You don't have to keep impressing us.
I do like your comic edits even though they could be construed as "showing off".

>>11103199
>using big words because you need to convince people you are smart

>>11103246
this.
I say we all upload scat and gore until the yukari tranny leaves 4chan for good.

>>11101079
I don't say suffering because it's hard, I say suffering because it's absolute dogshit as a subject.
>>11103082
Yukarihomo is absolutely hilarious. By far one of the best shitposters in this board.
It only looks autistic if you're the kind of autist who'd seriously consider showing off his amazing knowledge of PhD-level reformulations of basic physics in an amazonian jungle-burning board.

I'm trying to use induction and want to show that the RHS equals the LHS. Any tips/solution? Tried using common denominator to add but didn't get anywhere.
[math]\frac{2^{k+2}+(-1)^{k+1}}{3(2)^{k+1}}=\frac{2^{k+1}+(-1)^{k}}{3(2)^{k}}+(\frac{-1}{2})^{k+1}[/math]

>>11103963
You should get somewhere if you take a common denominator. Once you collect the right hand side over a denominator of 3(2)^{k+1}, you're left proving the numerators are the same on both sides, i.e. [math]2^{k+2}+(-1)^{k+1} = 2^{k+2}+2(-1)^k+3(-1)^{k+1}[/math], which is completely obvious.

>>11103246
Yukarifag solves problems constantly idiot. They're a better poster than all the tripfags on this board
>>11103821
you have low verbal iq and your parents deserve to be whipped in public for never making you read as a child

>>11103866
>>11104042
is he samefagging or is there actually a defense force for an avatarfag in a math general

>>11104042
I don't think I've ever noticed a tripfag on the bored. Most of the name fags are huge fags though especially solivagus

>>11104050
fuck you self-hating nigger

Not math.

When doing related rates problems, how do you know when to convert to radians? Is it true for any implicit differentiation where theta is being differentiated with respect to time? One of my problems was wrong until I converted to radians, but I just did another with a constant angle and it was not necessary

Is it odd that a professor would skip the hyperbolic functions section in a calculus 1 course?

>>11103491
Check out persistent homology and topological data analysis. ML is becoming increasingly useful in stat mech as well.
We do need people to crunch the numbers after all.

hey i'm the guy who originally posted the weak* definition lacking full generality and i want to emphasize that most of you people are fucking idiots and that yukariposter is a great boon for the board and for /mg/ and /sqt/
i only meant to make sure the original guy who asked wasn't confused by how yukariposter's response to my definition was phrased. i hold no ill will toward yukariposter and actually appreciated the opportunity to learn about the weak* topology as it applies to operators.
since i am learning operator algebras and such at an early graduate level now, i can say with partial certainty that yukariposter generally knows what they are talking about when it comes to operator algebras and QM, as well as with differential geometry and its noncommutative equivalents. i greatly appreciate having someone with this perspective and background on /mg/ as someone who finds the field fascinating.
and also that shit isn't that hard to learn, i've been doing it for like a year and i know plenty of what the dude talks about, i'm sure any competent grad student who is looking at mathematical physics would easily comprehend most of yukariposter's expositions and responses.

>>11103188
okay nevermind i'm this guy >>11104270 and this kind of annoys me
read the fucking thread for christs sake, it's not that long

How do i get a math nerd bf

>>11104381
i want a math jock bf

>>11104381
can it be femboy?

>>11104394
>>11104387
As long as it's subby

>>11104405
<3 they're out there anon

>>11104405
I'm out there anon

>>11104405
no i want to be the subby

>>11104394
>>11104405
>>11104410
>>11104415
>>11104418
this board is gayer than /lgbt/….

>>11104410
>>11104415
>>11104418
>tfw still no twink switch math bf to make me feel ok with being sissy

>>11104422
not gayer than /int/ though

>>11104381
Be at least a 6/10 biological female and talk to any math nerd.

>>11104270
Neither of my points includes that yukariposter doesn't know what he is talking about, nor that his explanations are incomprehensible even to people that know mathematical physics.

My question is, when you asked the question did you want to hear that continuity of operators and boundedness of them is linked to the Banachness of the space?
It seemed to me irrelevant to your question, or even what you wanted to talk about.

>>11104504
i'm referring to other people's posts when i say that. and no, i did not want to hear about that, in fact i was quite aware of it, but i certainly don't mind hearing about it as much as you seem to. again, i just wanted to clarify that it was not relevant to the person who originally asked.

>>11104381
Open a latex editor and type \mathbf to get your own \mathbb.

>>11104422
>this board is gayer than /lgbt/….
>/lgbt/
You mean /tttt/? There's nothing gay on that whole board. There are only trannies.

>>11104564
trannys are gay, this board probably has more trannys than /lgbt/ as well. UwU is pretty much a /sci/ meme now

>>11103086
They are major part of the rationalist community. They disillusioned Qiaochu from pure mathematics. He works in machine learning today which is especially big with the rationalists (see Roko's Basilisk).

Is wildberger's math foundation series a good guide for self-study?

>>11103246
>them
>>11104042
>They're
What did she mean by this?

>>11094565
How do I get better at maths? I barely passed it throughout high school and I'm about to start studying Computer Science.

Programming is no problem for me since I've been doing it for years, however maths is something I know I'll struggle with quite a bit. I want to start taking it more seriously since I also find it very interesting.

>>11104948
>Programming is no problem for me since I've been doing it for years
It's the same for math, you need practice. It's more difficult since in programming you kind of know what you want and if it doesn't work in the end you did something wrong. With math you cannot simply test whether your thoughts are wrong or not. My advice would be do not get memed into too abstract math too early since arithmetic skill is actually more important than you might expect when looking at "modern" math.

>>11104956
Thank you that is helpful.

>>11103082
based

>>11104148
hyperbolic trig functions are just regular trig functions rotated in the complex plane

>>11104797
Yes.

How do I get the most out of visiting the lectures?
The professors do upload scripts after every lecture so I dont have to write everything down.

How many notes do you take?
Do you take notes at all?
Do you follow a specific approach when taking notes?

>>11105049
>he attends lectures

>>11105055
Attending lectures gives me structure in my life. This is very important for me since I do have ADHD.
Its somewhat good for socialising. This is very important for me too since I struggle with Aspergers.
Im a first semester student and the professor explains the notations which is helpfull, because the script is easier to understand that way.

>>11104042
>refers to himself as they
Why dont you let me find out where you live so I can stomp your face out tranny

>>11105080
I would rip your eyes out of their sockets if you spoke to me like that irl faggot

>>11105071
Then I won't judge you.

>>11104648
>They disillusioned Qiaochu from pure mathematics.
Could you explain how or link to some posts?

>>11105109
You wouldn't do shit, you mentally ill freak.

Can you see the symplectic group as the group of linear transformation preserving a certain kind of "scalar product" (namely, an alternating billear form), or is this a an error of intuition ?

>>11105080
Not him, but that's my kink

Can /mg/ find the hypotenuse of this triangle?

>>11104422
/lgbt/ is full of gays and trannies
/mg/ is full of faggots and faggot trannies

learn the difference

>>11105296
sqrt(2)

>>11105296
>Can /mg/ find the hypotenuse of this triangle?
[math] |1+i|=\sqrt{2} [/math]

>>11105197
dude that's precisely what it is. (don't think of a symplectic form as a scalar product though).

How should I be thinking of factor rings? Why is whatever that is being "factored" equivalent to 0. Is there any systematic way of thinking about the elements of a factor ring?

>>11105139
why dont you just look it the fuck up you fucking moron
basically he woke up one morning and went "eh"
posts in stack about it

>>11105285
>him
I'm not a "him."

>>11105333
yes, the fucking definition. for an ideal I in a ring R, think of elements of R/I as x + I for some x in R. then of course 0 + I is just I. so everything in I is sent to the zero element in R/I (which is 0 + I)

>>11105369
kys faggot

>>11105109
Sure you would you little faggot. The moment I see you going for my eyes, I would unironically beat you to death while you cower on the ground like the little bitch you are. I work at the airport so I can fly anywhere. Why dont we meet up.

>>11105369
Why do you do this ?
What is there to gain here

The class of non-isomorphic groups is proper because it contains the free groups which are in bijection with the class of all cardinals. Is this the only thing preventing the class from being a set? That is, is the class of all non-isomorphic, non-free groups proper?

>>11105646
>class of non-isomorphic groups
What do you mean by non-isomorphic ?

>>11105333
You're looking at wrong, the definition of an ideal is *exactly* what it needs to be such that as cosets it behaves as the additive identity.
>it's a subring, that is, for a, b in I a + b and ab are in I (0 + 0 = 0 and 0 * 0 = 0)
>it's an ideal, so for any r in R and i in I ri and ir are in I (0 * x = x * 0 = 0)

>>11105652
the class of all groups under the equivalence relation "is isomorphic to"

>>11105652
If you mean the class of isomorphism classes of groups, then yes you can find isomorphism classes of groups of arbitrarily large cardinality and they do not have to be free.
For example, for any infinite set X, the set of permutations of X with finite support has the same cardinality as X and is not free, since it has many finite subgroups (whereas any non identity element of a free group has infinite order)

>>11105670
I see. thanks.

Does anyone have the pic of a anime girl and ENS logo on it

What to you is the most interesting/deep/bizarre/etc. theorem in set theory?

>>11105049
Furiously transcribing a set of notes is largely a waste of time, and they're a complete waste of time in undergraduate classes since anything you could possibly need to refer to again is in the book anyway. The only effect notetaking has is distracting you from actually focusing on the lecture being given.
People only take notes because this is what they've been taught they have to do in classes since elementary school.

>>11105734
>The only effect notetaking has is distracting you from actually focusing on the lecture being given.
This has been discussed time and time again and, no, that's absolutely not true.
Obviously, you should not be writing down every single thing and focus on what is happening during the lecture, but writing things down helps solidify them in your mind and anchor you in the lecture. At least if you start drifting off, you have something to do. If you take no notes, then you might understand everything, but you could also get lost at one point, and then have your eyes glaze over for an hour.
The idea that proficiency is somehow correlated to whether or not you take notes is a myth. Some people do without notes, but many people do with, and do very well. Most mathematicians I know take notes during talks or lectures, if only for future reference. They do it efficiently, but they do it.

>>11105646
Can't you just take all cardinals, order them by the axiom of choice and consider the all group of shifts within these listson.

>>11105750
Instead of developing coping mechanisms for the fact that you can't focus on a lecture for an hour without spacing out, maybe address your ADD?

>>11105701
For a meta-theorem, note that the following is independent of ZFC:
>"Given a set B with a bigger cardinality than a smaller set S, then the set B also has more subsets than S."

>Set theory in charge of capturing the notion of collection

>>11105762
what's a meta-theorem

>>11105761
take a real math course and get back to us how much you retain.

>>11105781
>resorts to ad hominems because his original argument was "take notes because focusing for an hour is really hard"

>>11105789
how's college algebra treating you?

>>11105797
Pretty good. Since I don't have a learning disability I easily stayed anchored the entire lecture, and my eyes didn't glaze over at all.

>>11105801
cool. now go take a real course and see how it works out for you.

>>11105805
Cope harder brainlet

>>11105808
doesn't really matter what you say. reality will do all the proving it needs to when the time comes.

>>11105813
>NOOOO I'M NOT HANDICAPPED YOU'RE JUST A FRESHMAN

>>11105574
choke on a tailpipe nigger

>>11105815
like I said, which isn't that hostile of a request - go take a real math course and see how it works out. this is not too much to ask, is it?

>>11105822
>Y-YOU'LL SEE, NO ONE CAN FOCUS ON REAL ANALYSIS FOR AN HOUR

>>11105822
there are a large number of students that don’t take notes and still earn A’s retard

>>11105824
not an argument
>>11105825
I'm sure they take notes, just not in lecture.

>>11105829
>not an argument
neither is "everyone who disagrees with me is enrolled in college algebra" but you don't seem particularly bothered by that one

>>11105834
neither is "you must have ADD"

>>11105837
True, that's not an argument, it's an observation based on your admission that without something to occupy yourself your eyes glaze over for an hour in class

>>11105838
well, hate to break it to you but I'm not the original guy you've been "arguing" with. he probably got as fed up as I'm getting with your trite.

>>11105847
>m-merely not me
shifting into maximum damage control

>>11105849
anonymous image boards are like that, reddit.

>>11105774
https://en.wikipedia.org/wiki/Metatheorem

Example:

>2+3=5
This is an example of a Theorem of first order Peano Arithmetic.
This is the theory that has the set of ordered natural numbers [math] \omega [/math] as a model, and which postulates a dozen equalities that express intuitions about successive numbers. Addition and multiplication can be defined in this system, as what amounts to recursive equalities.
E.g.
[math] n+(k+1)=(n+1)+k [/math]

>2+3 != 17
This is an example of a Theorem of first order Peano Arithmetic, also.

>2+3 = 17 has no proof in Peano Arithmetic
This is an example of a Meta-Theorem of Gentzens logic with assumed existence of ordinals up to
[math] \omega^{ \omega^{ \omega^{\cdot^{\cdot^\cdot}}}} [/math]
This amounts to a theory of infinitely deep trees of countable nodes.
This isn't a theory of arithmetic, since you didn't say anything about addition and multiplication, but -as it turns out- you can use it to embed Peano Arithmetic proofs (sequences of symbols) into those trees, and then express the consistency of Peano Arithmetic as a statement of those trees.

Thus, in the end, assuming this tree logic, you find Peano Arithmetic is consistent and there's no proof of both
>2+3 != 17
and
>2+3 = 17
too.

This is a meta-theory about another theory. The theory of arithmetic is about numbers, it doesn't apriori (and, as it turn out can't itself, as Gödel found) speak about it's own properties as a theory.

>>11105817
Come on bitch. What are you scared of talking tough on the internet. I can fly anywhere for free since I work at the airport. Give me a location and i can meet you there within a week.

>>11105761
My class taking days are behind me, my friend, but I have been doing very well for myself, still taking notes when reading books or articles, or when attending talks.
Again, most professors I know (even those very established in their field) take notes during talks they are interested in. I think it is fair to assume that it is not a hindrance to learning.
Now I have to ask, why are you so defensive ?

Is there a well defined tetration operation for cardinals, where tetration of a real number [math]a[/math] is defined [eqn] {}^{n}a = \begin{cases} 1 & \text{ if } n=0 \\ a^{\left( {}^{n-1}a \right)} & \text{ if } n>0 \end{cases} [/eqn] . For example, [math]2^{3} = 2\cdot 2\cdot 2 = 8 [/math], while [math]{}^{3}2 = 2^{2^{2}} = 2^{4} = 16 [/math] ? If so, is it useful/interesting?

>>11106285
Looks like a perfectly find recursive definition involving exponentiation.

>>11105296
It seems intuitively clear that it should be the square root of 2, after all C is basically just R^2.

>>11106324
Though how exactly would it work for say [math]{}^{\aleph_{0}}\aleph_{0}[/math] ?

I've been trying to this for over an hour but I'm stuck.
Suppose I have a function u: R^n -> R such that u(x) = v(r) with r = ||x||. How do I compute the Laplacian of u in terms of v and r? I know I should use the chain rule but I keep getting stuck

is teaching at the hs level worth the pay?

>>11107024
yes

>part of the homework is graphing
>have a trackpad
brb, writing my manifesto

Can you show uniqueness for F?

$$h(t)=\int_t^ag(z)(F(z)-F(t))^n \; dF(z) $$

>>11106829
Compute the total derivative and compare the partials of the composition ot the chain rule, then do the same foreach coordinate function.

>>11106829
Write the Laplacian in spherical coordinates.

>>11107110
Cant use spherical coordinates because it’s in R^n
Can someone tell me where I went wrong??

>>11107024
Depends on the situation. If you're in an average, functional high school, and you have enough balls that a bunch of little 14 year old asshats will respect you enough to sit the fuck down and shut up for half an hour, then yeah, it's a nice, mid-low stress job that pays pretty well and is occasionally somewhat fulfilling.
If you get stuck in a shit school with impossible-to-manage classes, or you're a stuttering pussy and kids don't care what you tell them, then it's an incredibly shitty job.

>>11107170
>Cant use spherical coordinates because it’s in R^n
Ah yes the famous celebrated result "spheres don't exist in dimensions [math]>n[/math]."

>>11107179
My bad I'm pretty tired... what I meant is that i don't know how to use spherical coordinates in n-dimensions bc im dumb

>>11107182
In general [math]\mathbb{R}^n[/math] if something depends only on [math]|x|[/math] then it's symmetric under [math]O(n)[/math], the action of which fixes spheres of radii [math]r = |x|[/math]. These spheres [math]S^{n-1}[/math] can be parameterized with [math]n-1[/math] Euler angles [math]\boldsymbol{\varphi}[/math] (say), hence spherical coordinates in [math]\mathbb{R}^n[/math] can be written as [math](r,\boldsymbol{\varphi})[/math].
Now the Laplacian [math]\Delta[/math] is [math]O(n)[/math]-invariant, i.e. [math][\Delta,O(\boldsymbol{\varphi})] = 0[/math] for all [math]O(\boldsymbol{\varphi})\in O(n)[/math], hence [math]\Delta[/math] is itself independent of [math]\boldsymbol{\varphi}[/math], and only depends only [math]r[/math]. You can then just find the scaling factors in [math]r[/math] from e.g. the first row of the Jacobian [math]J[/math] of the coordinate transform [math]x\mapsto (r,\boldsymbol{\varphi})[/math], and use [math]\partial_i = J_{ir}^{-1}(x)\partial_r[/math] to find the explicit form of [math]\Delta[/math].

>>11107182
The spherical Laplacian will look like a sum of the radial part of the Laplacian and the Laplacian on the sphere. In your case, the Laplacian you seek to calculate takes a simple form since your function is radial. So you don't really need to even know what the Laplacian on the sphere even looks like anyways.

>>11107170
>>11107182
there are spherical coordinates in R^n, which look like the spherical coordinates in R^2 and R^3 (polar and standard spherical respectively)

is this feasible to learn in ~2 months with no trig experience, just geometry (years ago) and algebra?

>>11107219
Yes.
You'll have to do a lot of practice problems though.

>>11107219
if your algebra skills are fairly solid, and you don't have much else going on in your life so that you can focus pretty much only on this, then it might be possible
otherwise no

>>11107219
>closed graph theorem and corollaries/equivalents
>polynomial rings and fields of fractions
>the exponential and logarithm maps on manifolds
>fourier analysis
>linear programming and convex optimization
>linear algebra
>real analysis and measure theory
>algebraic geometry
sounds pretty easy to me

>>11107219
No, you will burn out within a week if you try to keep up the pace you need.

>>11107298
Why do you mention unrelated topics which have nothing to do with that highschool math curriculum?

>>11107310
i was under the impression those are the topics that were being covered? did you look at the picture for even a moment?

>>11107170
Just calculate correctly.
And ignore advice from people who clearly didn't do the exercise and are just speculating.

>>11107215
>>11107208
>>11107195
>>11107110
Don't use spherical coordinates and stop giving garbage advice, the calculation is straight forward.

>>11107336
>i was under the impression those are the topics that were being covered?
No, they aren't. It's clearly a basic highschool math book.
Have you looked at the picture for a second?
It goes up to basic linear algebra, nothing more advanced.

>>11106341
Ah well, I didn't take the n's to be cardinals too. If you let n be ordinals, maybe
https://en.wikipedia.org/wiki/Transfinite_induction#Transfinite_recursion
makes may make sense here - give it a try.

>>11107182
https://en.wikipedia.org/wiki/Del_in_cylindrical_and_spherical_coordinates

>>11107350
Good little engineer.

>>11107357
>https://en.wikipedia.org/wiki/Del_in_cylindrical_and_spherical_coordinates
Stop giving bad advice. The calculation is straight forward in Cartesian coordinates.

>>11107360
>Stop giving bad advice.
What's the advice here? Stop being agressive, shall he do with the resource what he makes

>>11107358
???
If you have done and course on PDEs this calculation is literally straight forward.
But you idiots apparently didn't manage it so you got some guy to waste his time because he made a basic derivative error (which none of you pointed out).
Btw I actually have a math degree...

>>11107363
>What's the advice here?
That he should use polar coordinates.
He shouldn't and stop pretending it will help him.

>>11107364
If you had done any decent non-engineer oriented course in PDEs you'd know that understanding PDEs require a strong geometric intuition (e.g. the min-max principle, weak solutions and optimization problems). The reason spherical coordinates is preferable here is because it puts the Laplacian (restricted to [math]O(3)[/math]-invariant functions) in geometric context, instead of just pure numbercrunching crankturning. If this is all you can manage then suit yourself, but don't think you can poison someone else just because you never had to learn anything interesting.

>>11107368
You are literally retarded.
Obviously I know all of these things but it's irrelevant. The guy made a basic error and instead of pointing it out you told him that he should transform his trivial problem.

Stop justifying your idiocy.

>The reason spherical coordinates is preferable here is because it puts the Laplacian (restricted to O(3)-invariant functions) in geometric context, instead of just pure numbercrunching crankturning.
You are delusional.
The result has to be geometrically interpreted, but not the fucking calculation.
Shut the fuck up undergrad.

>>11107374
>intuition doesn't facilitate computations
Ask me how I know you've never done any research in any field.

>>11107377
Whatever, undergrad, your deep geometric interpretation of a trivial question impresses us all.

>>11107378
Yikes.

>>11107380
Yes, yikes indeed.
Continue your research into how you can geometrically interpret the solution of babies first PDE problem.

>>11107383
Just stop dude holy shit.

>>11107385
I didn't start this.
You guys couldn't solve babies first PDE Problem abd are now coping.

>>11107358
>>11107368
>>11107377
the absolute state of this general

how come this was so dead today