/mg/ maths general; Langlands Edition

Will he ever publish?

How to sketch and visualize vector functions? I'm studying multivariable calc and this is the hardest part to me

Any tips?

How would I go about proving that Ɛ'(U) is the dual space of C^∞(U)?

I know that I need to show that F ε Ɛ'(U) extends uniquely to a continuous linear functional on C^∞(U) and if G is a continuous linear functional on C^∞(U) , then G|Cc^∞(U) ε Ɛ'(U).

Please PLEASE help me anime math gods.

We am a mathematician after all, not a computer scientist.

The accumulated filth of all their analysis and applied mathematics will foam up about their waists and all the whores and physicists will look up and shout "Please PLEASE help me anime math gods!"... and I'll look down and whisper "No.”

vector fields

at some point in space your function gives you three values, which correspond to the magnitudes of a vector in your basis, therefore by plotting multiple such points you will obtain vectors showing you some "streamlines" that would take some test particle and flow it throughout the field like a river

modify dimensions from this most important case and you can visualise anything

group theory exam today, I think I'm fucked. wish me luck

Is he a hack?

>applied "mathematics"

>xd anime and math
>xd go bagg to rebbit
>xd i gate fisics

9565799
Stop being a retarded newfag and people will stop telling you to fuck off to where you belong.

Do you need to swear?

I think it's only (you) user.

>i'm fresh out of reddit the post

In what fucking way you brainlet?

wrong matrix, don't bully me pls
\begin{bmatrix} & 1 \\ 0 & 0 \end{bmatrix}
*blocks your linear algebra*

last attempt at this shitpost
[eqn]\begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}[/eqn]
*BLOCKS YOUR LINEAR ALGEBRA*

You failed twice, impressive

You forgot
>xd I am so depresd
>xd I wannuh suk a cock

third time's the charm x

Your people are not welcome around here. I suggest using .

See

>posts math content
>"reee get out!"
lmao, keep posting, this is entertaining.

Who are you quoting?

>HURR LET ME POST PHYSICS IN A MATH THREAD

>reee
>lmao
see >HURR
>LMAO
see

It's not my fault anything that involves vector/tensor calc, representation theory, PDE and the like is treated as physics here.

>he can't into group theory applications to QM
massive brainlet detected.

I've never seen representation theory treated as physics here, what posts are you referring to?

>vector/tensor calc
>PDE
Please refer to the proper board for discussing physics.
>QM
I'm sure they would like to discuss that with you in the physics threads over at .

Well one time I posted some shit about the Lorentz group, and everyone got triggered. Though, now it's mainly this shitposter

Redirecting people to proper discussion boards is shitposting? Is your severe level of brain damage due to physics?

A yes, /toy/ the place for discussing mathematical physics.

best not to argue with "it" m8, gets nowhere. Pretty sure it's mentally ill.

It doesn't matter what adjectives you decide to attach to "physics". That won't make /mg/ an appropriate place to discuss it. I recommend using or trying to create your own "mathematical physics" imageboard.

>I recommend using or trying to create your own "mathematical physics" imageboard.
Mathematicians use "we", not "I".

I bet this handsome motherfucker triggers the lot of you

Explain the relation between math and sissybois right now.

People usually don't get "triggered" by animals.

>I don't know how to answer your question

Who are you quoting?

The post I linked

As a mathematician we would not use "I" in our post, what you quoted with an "I" in it must be in a different post.

have this:

a1 = {2;3}
a2 = {3,5,7}
a3 = {1,7}
a4 = {3,8}
a5 = {9,3}
a6 = {6,4}
a* = {...}

As you can see, 3 is them most common number. What would be the formula to find it? I assume it exist, so wiki link work too.

>a* = {...}

...what?

What is "a* = {...}" supposed to mean?

anything that first the criteria, imagine

a7 = {1,5};
a8 etc

It was just an example, you can take first 6

There's no "formula" for such a thing that would be anything other than a trivial rephrasing of "most common number".

And it's also not even necessarily well-defined.

So in other words you are stating such task cannot be solved by math (any kind of math, any category)?

Imagine context: an apartments house of 100 rooms. Each occupied by 1 resident. In March, between march 19 march 25, there is an apartment-wide meeting but the organizers need to decide which day of a week to pick up so they cover majority of the people.
So, 7 days a week. They call each one and ask which day(s) these find acceptable. One guy says Monday and Friday, so:
a1 = {1, 5} (2 days out of max 7)

This is context. Now, there are 10 or 100 variables, for example, we need to do math to find out the most common day for each.

you could define a function [math] f: \{1,2,3,4,5\} \to \mathbb{N} [/math] with [math] f(i)= \text{# of people free on day }i[/math] and then the most common days to be the set [math]\{j \mid f(j)=max_{k=1,2,3,4,5} f(k)\} [/math], but this is just a restatement of 'most common elements'

>So in other words you are stating such task cannot be solved by math (any kind of math, any category)?
No, he is saying that the formula is obvious.
You might be looking for an "algorithm", a computation for that maximum.

so that
would be an algorithm?

Nope, big fan here. I don't even work in his area but you gotta recognize raw talent

>would be an algorithm?
No, that is a "mathematical description".

An algorithm is usually stated in some form of "pseudo programming language", in which the steps to acquire the wanted results are described.

Damn i was hoping for some magic "math function" where you crunch some numbers and get an answer, at least approximate.

I can write simple for loop in prog. language no problem

How is "raw talent" in things unrelated to mathematics somehow relevant to this thread? Maybe we should start discussing raw talent in music and painting here as well?

Well, think about it: How would you even answer the problem without at the very least reading every single letter, since you don't have any other assumptions about the distribution of the numbers in the set?

The best you can do is scan over all of them and keep count. This is an information-theoretic lower bound of Omega(n) assuming n elements.

Why did you think that could work?
Looking at every set once is the trivial solution, although there is some trickery you could do to speed up the process.

> at least approximate
Quit your loop after a few steps, then you have a "good guess" (although it could be completely false) at what the maximum could be.
eg. just look at a1 and a2, the result will be 3.

You don't necessarily need to look at every element, if one number turns up often enough you can terminate early.
But to be honest there is little point in actually doing it.

>Why did you think that could work?
I dunno, some math magic like, summarize all values for each An and then divide by some magic stuff so the final results will be close to most common number

>I dunno, some math magic like, summarize all values for each An and then divide by some magic stuff so the final results will be close to most common number
But that is just as complicated as just going through the list, I am not aware of any magic that could make the computation easier.

>But that is just as complicated as just going through the list, I am not aware of any magic that could make the computation easier.
I think it is easier to do a sum of number and then division on calculator rather than going through 10+ entries and trying to determine most common number manually. 10 may be not a big deal, but 50? mechanical math operation with calculator is simpler

Anyone else getting fucked by complex analysis? Shit's hard, yo

Same reason walking backwards is harder than going forwards

Nigger do you even know how Arnold is?
es.m.wikipedia.org/wiki/Vladímir_Arnold

They are just harder to compute analitically. But they are pretty easy to understand.

Well, that might be the case, but calculating the average won't help you much here.
I doubt that you can do much beyond the trivial, counting how many time each number appears.
Anyway, that is what computers are for, I suggest that if you are facing this problem in realty a computer will, with a trivial algorithm will give you the quickest answer.

>but calculating the average won't help you much here.
Dont be silly, sweetie, the average was just an example.

Question was theoretical, there is no task at hand, I was just curious if some gurus of Calculus (math analysis) can think of something that can produce desired results.

>I was just curious if some gurus of Calculus (math analysis) can think of something that can produce desired results
This has very little to do with calculus.
If you are interested in an efficient algorithm, then go ask people who do CS.

Will applied math + statistics degree get me a job? My dumbass parents say no cuz it will be automated in the future and want me to do cs

No, but his ego is bigger than even Motl's and much more fragile.

Is there any way to prove that
[math](a=b)\iff (a+c = b+c)[/math]
from the field axioms of the real numbers? (or for abelian groups in general)

Also, even in proof-heavy calculus 1 courses we use stuff like

given that a=5
then the equation a + 6 = x is equal to 5 + 6 = x. Why is that so?

Motl has never been wrong, he earned his ego

it's funny because it is the opposite for a computer, i.e., finding integrals is easier.

I suppose you know that the general procedure is to add (-c) to both sides and associate and whatever. It's called the canceletion law and it's valid even for non commutative groups. But your question seems about the "preservation of equality". Assuming you are going with spivack, this comes from tricotomy of the total order ir whatever axioms you are using. If you are going even more specific, the equality is equality of sets, and you can construct the real numbers just using set theory. But jusy finish chapter 1 quickly, as it's just a way to introduce proofs.

>=>
>a=b
>add c to both sides
>a+c=b+c
>a+c=b+c
>cut c from both sides
>a=b
>qde
no need to thank me

Not using Spivak as "The Book", but I definitely check it for some definitions and obviously solve the problems.

How can you add (-c) to both sides? Doing that results in a redundant proof, since that's what you want to prove.

I know about the tricotomy of the total order, a>b, a=b or a>b. But how that results in being able to "insert" equivalent values on the terms of your equation?

Basically, why (4/2)+x = 1 can be expressible as 2+x = 1

I understand that the 'preservation of equality' can be proven through the cancellation law. But how can you prove the cancellation law itself?

Well, what axioms are you using? If it's synthetic approach, you usually start by saying that the order is preserved under addition. For groups, in the abstract, you have that if a=b then ac=bc comes from the fact that the operation is a function from GXG to G, and if that wasn't the case the function would not be well defined.

I'd love some more explanation (or books I could read) on the abstract algebra explanation you gave.

But for the axioms we're using, order axioms are:
1) The order relation is a total order (which, to me, can be proven defining a>b as "the difference between a and b belongs to the positive numbers and thus is kinda forced)
2) If a>b then a+c>b+c
3) If a>b then ac > bc for c > 0

What now

K then, use 2) but insteas of > use = (total order means greater or equal). So just add -c...

>I understand that the 'preservation of equality' can be proven through the cancellation law.
No, it can't. There are plenty of examples of things that don't have cancellation but still have equality. Functions, for example, do not cancel, but if f = g then h o f = h o g.

In the cases where it holds you have to prove the cancellation law, and you do this by not being a jackass going
>hurr a=b but how do I know that a is b

I'm getting a letter of recommendation from a super handsome lecturer, but he's like 45 yo. Does this make him my sugar daddy? Good night, btw.

I got Cs in stats and pre calc in college. I never studied or went to class, but still its embarrassing. I now want to learn data analytics to help with my research job. I know this field requires linear algebra, statistics, and some calc. My plan is to start back in high school math for a refresher then move through working on MITonline courses. Then Ill buy whatever books I need to round out.
Any advice on relearning math? I'm shooting for 2 hours of practice a day until I get up to speed.

>been out of college for 4 years
>left off at calc 1
>have to relearn most of math in a few months
If I fucking cram, is it possible to get myself back into working order?

I messed around with some Riemann sums and limits on Khan, and kinda somehow did things I didn't remember learning.

Hey fags, any grad school kiddos here? What's the competition like? Will I BTFO everyone if I read the canon (Rudin's Analysis, Munkre's Topology, Knuth's Concrete Mathematics, etc) in addition to what I do in undergrad?
What are you trying to test into? You could pass Calc 1 with flying colors in that time.

Start with as high level as you're slightly uncomfortable with, fill in the gaps as you go. If I were you I'd start with a book like James Stewart's Calculus: Early Transcendental as a problem book review. Use Professor Leonard if you're stuck, along with the more well known resources that I asssume you know, like Paul's Notes, Khan Academy, 3Blue1Brown, etc. Try to work into Spivak, Apostol or Tao as soon as you're able, perhaps even in tandem.

Yes, just learn programming too and develop a lively github.

cuz differentiation has the chain rule and integration comes down to finding a closed formula for [math]\sum_{n=1}^\infty f(n) [/math]

>You don't necessarily need to look at every element, if one number turns up often enough you can terminate early.
But to be honest there is little point in actually doing it.

Okay, sure, you're correct. You need to look at least half the elements.

Thanks for the math advice I appreciate it.