/mg/ - Mathematics General

[Anonymous No.12464660]

Riemann Surfaces edition

talk maths, formerly >>12457035

[Anonymous No.12464662]

Math is gay

[Anonymous No.12464672]

>>12464660
Thanks, absolutely based.

[Anonymous No.12464674]

>the neighborhood of infinity

[Anonymous No.12464676]

Homotopybros please help

>>12461743

[Anonymous No.12464779]

The reals are fake.

[Anonymous No.12464804]

[math]
\begin{equation}
\begin{array}{l}
4^{x}+6^{x}=9^{x} \\
\left(2^{x}\right)^{2}+\left(2^{x}\right)\left(3^{x}\right)=\left(3^{x}\right)^{2} \\
\text { let } a=2^{x}, b=3^{x} \\
\text { then } a^{2}+a b=b^{2}, a, b \in \mathbb{R}_{>0} \\
a^{2}+a b-b^{2}=(a+i b)^{2}-2 a b i+a b \\
=(a+i b)^{2}-a b(2 i-1)=(a+i b)^{2}-a b\left(\sqrt{5} e^{i\left(\pi-t a n^{-1} 2\right)}\right) \cdots(1) \\
=(a+i b)^{2}-\left(\sqrt{a b \sqrt{5}} e^{i t a n^{-1} \varphi}\right)^{2}=X=0, \text { where } \varphi=\frac{1+\sqrt{5}}{2} \\
\operatorname{Re}(X)=a^{2}-b^{2}-a b \sqrt{5} \cos ^{2}\left(\tan ^{-1} \varphi\right)+a b \sqrt{5} \sin ^{2}\left(\tan ^{-1} \varphi\right) \cdots(2) \\
=a^{2}-b^{2}-\frac{\sqrt{5} a b}{11}((4-\sqrt{5})-(7-\sqrt{5})) \\
=a^{2}+\frac{3 \sqrt{5}}{11} a b-b^{2}=0 \\
\therefore a^{2}+\frac{3 \sqrt{5}}{4} a b=b^{2} \\
\therefore 4^{x}+6^{x}=9^{x} \Longleftrightarrow 4^{x}+\left(\frac{3 \sqrt{5}}{11}\right) 6^{x}=9^{x} \\
\therefore x \approx 1.1868 \Longleftrightarrow x \approx 0.7407 \quad(\perp) \\
\left((1): \frac{\tan ^{-1} 2}{2}=\tan ^{-1} \varphi^{-1}, \tan ^{-1} \varphi+\tan ^{-1} \varphi^{-1},=\frac{\pi}{2}\right) \\
\left((2): \cos ^{2}\left(\tan ^{-1} \varphi\right)=\frac{1}{\varphi^{2}+1}=\frac{4-\sqrt{5}}{11}, \sin ^{2}\left(\tan ^{-1} \varphi\right)=\frac{\varphi^{2}}{\varphi^{2}+1}=\frac{7-\sqrt{5}}{11}\right)
\end{array}
\end{equation}
[/math]
what's wrong with this

[Anonymous No.12464811]

[math]
\begin{equation}
\begin{array}{l}
4^{x}+6^{x}=9^{x} \\
\left(2^{x}\right)^{2}+\left(2^{x}\right)\left(3^{x}\right)=\left(3^{x}\right)^{2} \\
\text { let } a=2^{x}, b=3^{x} \\
\text { then } a^{2}+a b=b^{2}, a, b \in \mathbb{R}_{>0} \\
a^{2}+a b-b^{2}=(a+i b)^{2}-2 a b i+a b \\
=(a+i b)^{2}-a b(2 i-1)=(a+i b)^{2}-a b\left(\sqrt{5} e^{i\left(\pi-t a n^{-1} 2\right)}\right) \cdots(1) \\
=(a+i b)^{2}-\left(\sqrt{a b \sqrt{5}} e^{i t a n^{-1} \varphi}\right)^{2}=X=0, \text { where } \varphi=\frac{1+\sqrt{5}}{2} \\
\operatorname{Re}(X)=a^{2}-b^{2}-a b \sqrt{5} \cos ^{2}\left(\tan ^{-1} \varphi\right)+a b \sqrt{5} \sin ^{2}\left(\tan ^{-1} \varphi\right) \cdots(2) \\
=a^{2}-b^{2}-\frac{\sqrt{5} a b}{11}((4-\sqrt{5})-(7-\sqrt{5})) \\
=a^{2}+\frac{3 \sqrt{5}}{11} a b-b^{2}=0 \\
\therefore a^{2}+\frac{3 \sqrt{5}}{4} a b=b^{2} \\
\therefore 4^{x}+6^{x}=9^{x} \Longleftrightarrow 4^{x}+\left(\frac{3 \sqrt{5}}{11}\right) 6^{x}=9^{x} \\
\therefore x \approx 1.1868 \Longleftrightarrow x \approx 0.7407 \quad(\perp) \\
\left((1): \frac{\tan ^{-1} 2}{2}=\tan ^{-1} \varphi^{-1}, \tan ^{-1} \varphi+\tan ^{-1} \varphi^{-1},=\frac{\pi}{2}\right) \\
\left((2): \cos ^{2}\left(\tan ^{-1} \varphi\right)=\frac{1}{\varphi^{2}+1}=\frac{4-\sqrt{5}}{11}, \sin ^{2}\left(\tan ^{-1} \varphi\right)=\frac{\varphi^{2}}{\varphi^{2}+1}=\frac{7-\sqrt{5}}{11}\right)
\end{array}
\end{equation}
[/math]
what's wrong with this? I know there's a simpler solution using logarithm but I wanted to play with complex numbers and this is what I got.

[Anonymous No.12464815]

>>12464804
Nigga what the fuck did you do in (1)?

[Anonymous No.12464819]

>>12464815

[Anonymous No.12464820]

seventh for the completed infinite

[Anonymous No.12464865]

The best post ever made in /mg/.

[Anonymous No.12464879]

https://en.wikipedia.org/wiki/Middle-square_method

[Heliogabalus !lUw4zrCMeM No.12464932]

So /mg/ what is your profession?

[Anonymous No.12464941]

>>12464932
bumming on student gibs

[Anonymous No.12464996]

>>12464676
I've been been thinking about this, but I have no idea. I don't think I've seen one. Maybe it gives you a system of local coefficients.

>>12464865
Thanks!

[Anonymous No.12465016]

holy... based...

[Anonymous No.12465024]

>>12464932

[Anonymous No.12465056]

>>12464660
Hey anons. If I am trying to typeset a document in Latex is there a way that I can get it to automatically start new pages when I reach the bottom margin? I want to copy and paste natural language text from a Google doc into a Latex file, but I don't want to have to keep inserting new page for every page. Is there a way around this?

[Anonymous No.12465093]

>>12465056
It should automatically make a new page for you. Wtf are you doin?

[Anonymous No.12465120]

>>12464932
My profession is that of an esoteric scholar and recluse. I am a historian and down-dateman of mystical lore. I have been a student of the occult sciences for many years, and have penetrated to those realms which most people call supernatural.

[Anonymous No.12465140]

>>12464932
>Heliogabalus
I don't abide tripfags, but I give credit where credit is due. Based tranny emperor.

[Anonymous No.12465177]

>>12465093
O fugg, I must be doing something retarded

[Anonymous No.12465194]

https://lichess.org/rcFLpqy2

[Anonymous No.12465213]

>>12465194
fuck off chesstard

[Anonymous No.12465283]

>>12465177
Post document structure without content so we can help.

[Anonymous No.12465294]

>>12464932
the grant collector
the scholarship receiver
the prize winner
this is my profession

[Anonymous No.12465295]

Dankeschoen anon

[Anonymous No.12465312]

>>12464819
Why is B=2a?

[Anonymous No.12465411]

>>12465312
circle theorem

[Anonymous No.12465575]

>>12464865
Do you have a crush on them because they posted actual math in this general?
Last thread you seemed very interested

[Anonymous No.12465602]

>>12465575
We promised to make a paper together

[Anonymous No.12465762]

>>12465602
That's super lewd, I didn't know animeposter was such a slut.

[Anonymous No.12465798]

Munkres is a meme

[Anonymous No.12465818]

>>12465798
nah it's not a meme but i learned fucking general topology and basic group theory up to quotient groups and now i'm fucking stuck whenever i try to read an algebraic topology book i don't understand shit with the proof that the fundamental group of the circle is homeomorphic to Z

i also don't understand shit with differential forms and the wedge number

man im really a brainlet

[Anonymous No.12465826]

>>12465798
What makes you say that?

[Anonymous No.12465847]

>>12465177
In case you need to change page, there's always the command \newpage

[Anonymous No.12465861]

It seems that for invertible 2x2 matrices [math]A_i[/math] and [math]X[/math]

[math]\det\big(\sum_{i=1}^n A_i+B\big) - \det\big(\sum_{i=1}^n A_i\big) = \det(B) + r[/math]
where
[math]r = {\mathrm{tr}}\big(\sum_{i=1}^n {\mathrm{adj}}(A_i)\cdot B\big)[/math]

with 'adj' the adjunct matrix (flipping components and dividing by the determinant)

I found the case for 2 matrices on SE and got the others by iterating from 2 to 3 and then guessing.
(Here the 2 matrices case https://math.stackexchange.com/questions/673934/expressing-the-determinant-of-a-sum-of-two-matrices))

Anybody seen this before?
Looks cumbersome to prove by induction but it's a helpful formula.

[Anonymous No.12465872]

>>12465861
How on earth is this helpful?

[Anonymous No.12465881]

I will be publishing a proof of the twin prime conjecture in early-to-mid 2021.

[Anonymous No.12465883]

>>12465872
Well, to compute determinants of the form
det(A+B)
where the determinants of A and B are simpler (in my case, they are unitary matrices or derivatives of them).
I'm starting to think the formula is a relative of Jacobi's formula, which would suggest it works for higher dimensions too..

[Anonymous No.12465893]

I'm trying studying analytic number theory, I'm still undergrad the Apostol's intro is fine? There are better (that means with higher exercises per topic density) alternatives?

[Anonymous No.12466000]

>>12465881
you better hurry up
i'm gonna be uploading mine to arxiv before christmas

[Anonymous No.12466003]

>>12466000
lmao

[Anonymous No.12466031]

>>12466000
a fucking full house

[Anonymous No.12466087]

>>12465881
>>12466000
Just in the 1/100000th chance this could actually be true, please include some kind of dogwhistle so we can recognize it's you.

[Anonymous No.12466090]

>>12465826
Topology is supposed to be a type of geometry but the only time (so far) the material has felt even vaguely geometric was in the section on the quotient topology.

[Anonymous No.12466102]

How do repeated Cartesian products work? Is there any difference between [math]A\times B\times C[/math] and [math]A\times (B\times C)[/math]? First one would be a Cartesian product between three sets and second one would be a Cartesian product between two sets.
Is there any situation where defining n-tuples as nested ordered pairs doesn't work?

[Anonymous No.12466138]

>>12466090
That sounds like a personal problem. If you’re getting filtered by Munkres you should just give up now.

[Anonymous No.12466145]

>>12466102
Cartesian product of three sets is usually not defined. Mathematicians use AxBxC as an abuse of notation to mean either (AxB)xC or Ax(BxC) depending on your preference. They're all turn out to be isomorphic using easy to define bijections, so it doesn't actually matter which one you use.
It's actually possible to define the product of three spaces, and there are many ways to do it, but it's useless when you can take the product of two twice.

[Anonymous No.12466148]

>>12466138
Wow mean. Don't give up, Munkres can be hard depending on your mathematical experience.

[Anonymous No.12466160]

>>12465411
Which circle theorem?

[Anonymous No.12466188]

>>12466160
What?

[Anonymous No.12466189]

>>12466102
>Is there any situation where defining n-tuples as nested ordered pairs doesn't work?
Exotic remark: For n-tuples [math]A^n=A\times A\times \cdots\times A[/math], one can go and define, as you suggest [math]A^{k+1}=A^k\times A[/math] recursively, with [math]A^1=A[/math]. but in that case you also have the alternative [math]A^n:=(\{0,1,2,\dots,n-1\}\to A)[/math]. I.e. the functions from [math]\{0,1\}[/math] to [math]A[/math] correspond to pairs in [math]A\times A[/math]. From a ZF perspective, the function definition is somewhat nicer in that it has smaller rank. In the recursive definition, you reach down deeper every time and at for some sets involving the product you then require Replacement.

[Anonymous No.12466205]

>>12466188
Sigh can you just tell me why B=2a

[Anonymous No.12466212]

>>12466160
Nevermind figured it out centercircumference

[Anonymous No.12466216]

>>12466189
>pic related
Me when calculating
[math]\lim_{n\to \infty} \sum_{k=1}^n 1/k![/math]

[Anonymous No.12466236]

>>12466216
One could also spin it in a way to tell the >>12466102 he should think in terms of universal properties (and this would be a case of a limit), then the question can't arise

[Anonymous No.12466241]

>>12466216
I don't get it. Isn't that limit equal to e - 1?

[Anonymous No.12466255]

>>12466241
I took it to mean sum over 1/k exclamation mark. Otherwise why start at n=1.
Then again, the ! is in the math brackets.

[Anonymous No.12466270]

>>12466205
Angles α and β intercept the same arc of the circle, but α is inscribed while β is central. So the inscribed angle theorem gives β = 2α.

[Anonymous No.12466281]

>>12466255
Ah, that does make more sense.

[Anonymous No.12466297]

Math bros, what do you tell your physics friends when they say physics is harder?
I usually just laugh at them and change the conversation because I dont really want to talk about it. I absolutely know that Im better than my friends in engineering, and when it comes to my friends in computer science its like Im a different species than them. But the thing is, I feel a bit insecure when it comes to my physics friends. Thankfully many of them tell me how difficult proofs are which makes me feel a little better. But I just am not sure if I am actually better than them. I dont know how hard physics is compared to math and so I dont really know how to treat my friends in physics. So what do you guys think?

[Anonymous No.12466306]

>>12466297
I know that I'm not better than anyone in a general sense, although I might be better at certain things. I value my friends as people and for the insights and inspiration their respective fields of study provide.

[Anonymous No.12466309]

>>12464660
How do I cite an entire field or refer to a body of literature in general? I am trying to write a paper on functional analysis, and I have to refer to some very general numerical methods that have been used in mathematical biology and control theory, but do not appear in the pure math literature. I just want to generally acknowledge that these tools have been used before, but primarily outside of pure math. I'm not citing any specific results, and I'm not even very familiar with control theory or mathematical biology. Do I need to provide a specific citation to like a survey article or encyclopedia entry, or is it fine if I just mention that these results can be found in the literature on control theory and mathematical biology?

[Anonymous No.12466316]

>>12466297
In short, the most ‘difficult’ areas of physics are as ‘difficult’ as the most ‘difficult’ (i.e. relatively unexplored) areas of mathematics. You can train an older mathematician to become a good physicist, but I’m not convinced you could train an older physicist to become a good mathematician.

[Anonymous No.12466340]

>>12464660
[0,2,0]=[0,0,20]

123/2

[0,1,1]
[0,5,0,5]
[0,6,1,5]

[Anonymous No.12466361]

Is there a formula for the volume of a tetrahedron in terms of the areas of its faces analogous to Hero's formula for the area of a triangle in terms of the lengths of its sides?

[Anonymous No.12466385]

>>12465177
>>12465411
>>12466188
>>12466255
Dubs.

>>12466000
Nice digits.

[Anonymous No.12466428]

bros i got a c in calc 1. how can i recover from here?

[Anonymous No.12466444]

>>12466428
study business

[Anonymous No.12466496]

>>12466444
Dangerously based.

[Anonymous No.12466533]

Can someone recommend papers about twin prime conjecture?
Proving bounds and shit like that

[Anonymous No.12466551]

>>12466385
Why do you do this

[Anonymous No.12466699]

>>12466428
I got a C in calc 1 last year, and it was actually so close that it would've been a D if I had gotten one more question wrong on the final.
I'm currently sitting at 92.5% in calc 2. Granted, I could still fail the final but it's definitely possible to recover.

[Anonymous No.12466731]

>>12465861
Doesn't hold for 3x3. Try it on a computer with random matrices

[Anonymous No.12466748]

>>12466428
I have tutored people from a C to a B and sometimes an A in Calc, and I am a drunk with no degree. So some extra attention definitely helps. I can't recommend the personal tutor route though, because it is way too expensive (unless you get me, then it's obviously completely worth it). If you do go that route, first see if you can get one for free or very cheap through your college (because you likely can), and then if not, try to hire someone in person, because online services gauge both parties.

But in college, there is a lot more opportunity to get one-on-one time with TAs or professors if you actively seek it out. The most common problem is that people wait too long before asking for help, so if you are worried now about not getting through a STEM degree, and you do decide to major in a math-heavy field, it could help you a lot to plan for some of these semi-regular sessions right from the start. Office hours aren't just for you . . . but they are whenever you're the only person there.

Also, you don't have to major in STEM. I'm assuming that's what you want to do, but if it isn't, then I assure you nobody will care one shit about a C in a Calculus class. And if money is what you're worried about, then >>12466444 is right. Math is not how you make the biggest bucks.

[Anonymous No.12466749]

https://www.youtube.com/watch?v=magyZ6AQwcc

Does MG beleive in magic? I believe in magic =P

[Anonymous No.12466776]

>>12464660
>be me, junior year engineering fag
>just turned in my differential equations final
>realize that that was the last math class I need to take
>I am now done with math classes
>18 years of a subject are done
>feel strangely empty inside
Any integrals for this feel?

[Anonymous No.12466827]

>>12465575
>category theory
>actual math
>>>/reddit/

[Anonymous No.12467009]

>>12466102
[math]A\times (B\times C) \ne (A\times B)\times C[/math] in general (same thing when you include [math]A\times B\times C[/math], they're all different) .
But the obvious bijection between them translate to isomorphism in any category, so that's why most analysists, algebraists and geometers work with them as if they were equal.

[Anonymous No.12467021]

>>12466776
Sure, calculate [eqn]\int_A \text{free time }d(free\ time)[/eqn] where [math]\mu(A)[/math] is non-zero

[Anonymous No.12467107]

Will learning about Mathematical Logic help me understand proofs in general? Can any anons redpill me about it?

[Anonymous No.12467114]

>>12466087
you must do this

[Anonymous No.12467119]

Which of these books should I focus for modular forms and elliptic curves, /mg/?

1. KOBLITZ, NEAL, Introduction to elliptic curves and modular forms, Graduate Texts in Mathematics, 97. Springer-Verlag, New York, 1993.

2. SLVERMAN, JOSEPH H., Advanced topics in the arithmetic of elliptic curves. Graduate Texts in Mathematics, 151. Springer-Verlag, New York, 1994.

3. SLVERMAN, JOSEPH H., The arithmetic of elliptic curves. Graduate Texts in Mathematics, 106. Springer-Verlag, New York, 1992.

4. DIAMOND, FRED; SHURMAN, JERRY., A first course in modular forms. Graduate Texts in Mathematics, 228. Springer-Verlag, New York, 2005.

5. DALE HUSEMOLLER, Elliptic curves, volume 111, Graduate Texts in Mathematics, Springer-Verlag, New York, second edition, 2004.

6. ZAGIER, D., Elliptic modular forms and their applications, Universitext, Springer, 2008.

7. LANG, S., Introduction to modular forms, Grund. Math. Wiss. 222, springer, 1995.

[Anonymous No.12467153]

>>12466776
differential equations is such a shit course.

[Anonymous No.12467216]

>>12466428
doesn't matter, calc III is the one you gottaa pay attention to.

[Anonymous No.12467408]

>>12466309
Where did you read that the method was used in math. biology? There must exist at least a book that explain the method lol

[Anonymous No.12467434]

>>12466309
there's no such thing as "citing an entire field or body of literature"
the best thing to do: find a book where your thing appears and cite it
but if you don't want to make the effort just mention it in your text and don't put any citations

[Anonymous No.12467453]

>>12467153
honestly felt like my college taught it out of order just to fuck with us
teaching it with linear algebra would also simplify things enormously, but they don't

[Anonymous No.12467493]

>>12466533
>>12466444
>>12466699
Checked
>>12466551
Sometimes digits are left unchecked and that makes me sad :(

Anons I'm thinking of doing a course on stochastic differential equations next semester. Do you recommend me doing functional analysis alongside with it or is it possible to understand SDES without?

[Anonymous No.12467503]

>>12467107
probably not
it's an autism pit of the likes you can hardly fathom.
all you need to know is that in a proof you take what you're given, and only what you're given and show it must imply the result as a consequence.
read a book on proofs if you want to understand that process.

[Anonymous No.12467527]

>>12466731
i kno

[Anonymous No.12467531]

>>12466776
>>18 years of a subject are done
what does that mean

[Anonymous No.12467533]

>>12467107
of course

[Anonymous No.12467570]

>>12466385
>>12467493
you are doing very important work
thank you sir

>>12467107
no

[Anonymous No.12467594]

>>12466297
Physics is way harder than math man.

[Anonymous No.12467607]

who was in the wrong here

[Anonymous No.12467721]

>>12467119
I haven't read a single one of those and couldn't care less about the subject.
But Grundlehren books are on average better than GTM books.

[Anonymous No.12467728]

>>12466297
Physics is as hard as mathematics, they're like in different maximal points of difficulty.
But what physicists do in general is not exactly what they're supposed to, which makes it less harder than what most mathematicians attempt to.
Most of what experimental physicists actually do is a joke.

Now if they think math is easier, tell then to read Witten's papers. If they could understand anything from there they'd know better about how hard math can get.

[Anonymous No.12467743]

Is there a quick but elementary way to prove that [math]\mathbb{R}^3[/math] with vector product forms a Lie Algebra?
I did opening up one triple product [math](a\times b)\times c[/math] and then it becomes crystal clear that a cyclic sum over [math](a, b, c)[/math] of this will be zero.

[Anonymous No.12467811]

>>12467607
Holy fuck, the autism

[Anonymous No.12467827]

>>12466297
physics is definitely harder

[Anonymous No.12467838]

>>12467721
Nah, nothing really tops Springer, they're the best!

[Anonymous No.12467840]

>>12466297
Doing physics Bsc. Hardest courses are the physics ones, not courses from the faculty of math. Problems in physics seem chaotic, and not in the theory sense.

[Anonymous No.12468021]

>>12467838
I have bad news for you. Grundlehren is springer too...

[Anonymous No.12468082]

>>12467811
He went to war

[Anonymous No.12468118]

Any symplectic geometry anons here? It's very far off my area so I don't want to spend too much time to properly learn it.
Is there a straightforward way to compute the moment map give some Lie Group action?
For a simple example let [math] G = A(1) [\math] the group of affine transformations on [math] \mathbb{R} [\math] (smallest nonabelian Lie group). And let [math] G [\math] act on [math] M =
T^{*} \mathbb{R} [\math] by cotangent lifts (i.e.[math] (a,b) \cdot (p,q) = (aq +b, p/a [\math]. Whats the common way to compute [math] J [\math] here?

[Anonymous No.12468185]

>>12467119
Diamond and Shurman, no question

[Anonymous No.12468193]

>>12466297
You sound like you are very early in your studies. I think it’s fair to say that neither you nor your friends have any idea what math or physics are actually like.
Also, find better friends with whom you won’t be engaging in dick measuring

[Anonymous No.12468234]

>>12468185
Can you explain why?

[Anonymous No.12468267]

>>12466000
post number in title or something

[Anonymous No.12468268]

>>12468234
I really admire books that manage to balance accessibility with depth. This one I think is a good example of that. It has a kind of leisurely feel to it but does not skimp on rigor of exposition, it has plenty of examples and manageable exercises, and it spells a lot of things out that would probably be cut in more advanced textbooks (including background material).

[Anonymous No.12468277]

>>12467743
that's pretty much the way to do it.

[Anonymous No.12468279]

>>12467743
well, expanding the triple product is a pretty elementary way of doing this, so there you go.

[Anonymous No.12468309]

>>12468118
I don't recall there being any other trick to it than finding a base for the Lie algebra, computing the vector fields induced on the manifold, computing a Hamiltonian function for each and then stitching them together into a moment map.
Probably just lack of knowledge on my part tho.

[Anonymous No.12468335]

Anyone else submitting grad school applications today? Holy shit the last week has been stressful.

[Anonymous No.12468398]

Support this
https://agrothendieck.github.io/

[Anonymous No.12468432]

>>12465818
read more munkres. if you're just on quotient topology you don't understand compactness and path connectedness.

also read the munkres chapters on homotopy

[Anonymous No.12468479]

>>12466776
lol engineering fags are all the same.

anon it feels really significant but you could have learned all that material in a few years of high school, and you probably don't understand it anyway.

[Anonymous No.12468523]

>>12468335
I submitted them a while ago. How many places did you apply to?

[Anonymous No.12468706]

>>12468335
yep
last minute gang gang

[Anonymous No.12468849]

Question from Tao's Analysis book:

>Definition 9.1.5 (ε-adherent points). Let X be a subset of R, let ε > 0, and let x ∈ R. We say that x is ε-adherent to X iff there exists a y ∈ X which is ε-close to x (i.e., |x − y| ≤ ε).

>Example 9.1.7. The point 1.1 is 0.5-adherent to the open interval (0, 1), but is not 0.1-adherent to this interval (why?). The point 1.1 is 0.5-adherent to the finite set {1, 2, 3}. The point 1 is 0.5-adherent to {1, 2, 3} (why?).

Using example 9.1.7 for point 1 and finite set {1,2,3}, x = 1, y = an element in {1,2,3} so x -1 or x-2 or x-3. 1-1 is 0, so is not greater than 0 and fails definition of epsilon > 0. 1-2 is 1, 1-3 is 2, where does he get 0.5?

[Anonymous No.12468857]

How many languages does /mg/ speak
For me, it's English Spanish asl and German. But I've been considering learning Finnish since it's probably more complicated than any of the ones I currently know

[Anonymous No.12468869]

>>12466444
what does that mean
accounting
excel spreadsheets
office paperwork
working copy machines

[Anonymous No.12468875]

>>12468857
english and portuguese
a bit of french too

[Anonymous No.12468878]

>>12468869
studying business is a meme
popped out of existence due to taylorism in the late 19th century. business doesn't teach you squat and several business schools have been sued because of it

[Anonymous No.12468880]

>>12468268
Thanks anon, I'll look into it.

[Anonymous No.12468888]

>>12466776
What engineering?
If electrical your first linear systems course will be all complex variables, which explains why so many barely pass the course.

Many schools require complex variables and PDE for EE types.

[Anonymous No.12468899]

>>12468857
Finnish, Swedish, English and I did study German and Latin back in the days, but those are really rusty.

>>12468335
>>12468523
>>12468706
The best of luck to all three of you!

[Anonymous No.12468907]

>>12468899
thanks m8
not too worried, worst case I do a masters instead of a PhD and aim again in a year or two. I hope my application would look more impressive by then

[Anonymous No.12468912]

>>12468857
American english, british english, australian english and some early modern english.

[Anonymous No.12469069]

>>12468849
Anon, [math]|1-1|=0\leq \epsilon = 0.5[/math]

[Anonymous No.12469452]

>>12468523
weirdo. imagine being efficient and giving yourself ample time to study for finals.
7 so far, just finishing my 8th (fucking word limits aaaaghh). 14 total.
>>12468706
you've got this! still plenty of time.

[Anonymous No.12469525]

>>12468857
English, Deutsche, et en peux de Francais. Ich wunschte ich konnte Japonais sprechen.

[Anonymous No.12469739]

Is this a working definition of limit?
>given series or sequence, its limit is N0 if for any N1, you can find a term that brings you closer to N0 than N1
How would computations be done on this?

[Anonymous No.12469797]

>>12469739
What if the limit of a sequence is in the sequence? (1,1,1,1...)

[Anonymous No.12469802]

>>12469797
But anon, the limit of your sequence is pi.

[Anonymous No.12469840]

>>12467743
>I did opening up
why did you mean by this

[Anonymous No.12469969]

according to wolfram alpha (x^2)/(x^2 - 4) is equal to 1 + 4/(x^2 - 4) but when I try to do the polynomial long division on paper i get 1 - 4/(x^2 - 4). Why is the remainder positive?

[Anonymous No.12470018]

The Wildberger posting on /sci/ is really getting out of hand, why not force another meme?

I had a back and forth with the Burger on his comment section a few days ago and I'm pretty convinced by now "his system" will never be formalized to an extend that anybody could actually establish which theorems hold in it and which doesn't. He'll remain the arbiter of his flavor of finitism.

>>12469969
[math]\frac{a}{a-b}-1 = \frac{a}{a-b}-\frac{a-b}{a-b}= \frac{a-(a-b)}{a-b}=\frac{b}{a-b}[/math]

[math]\frac{a}{a-b} = \frac{b}{a-b} + 1[/math]

[Anonymous No.12470026]

>>12470018
thank you!

[Anonymous No.12470064]

>>12469840
He expanded it out like an idiot and gradually cancelled terms out.

[Anonymous No.12470157]

Yeah come to think of it, the smoother variant to pin it down would be

[math]1=\frac{A+U}{A+U}=\frac{A}{A+U}+\frac{U}{A+U}[/math]

and let [math]A=x^2[/math] and [math]U=-4[/math].

which I now realize is a very specialized case of the matrix inversion lemma
https://en.wikipedia.org/wiki/Woodbury_matrix_identity

[math] \left(A + UCV \right)^{-1} = A^{-1} - A^{-1}U \left(C^{-1} + VA^{-1}U \right)^{-1} VA^{-1} [/math]

Which isn't unrelated to my question yesterday
>>12465861

[Anonymous No.12470254]

>>12469452
I gave up at 11 applications. Are you applying to only US schools are are you looking abroad?

[Anonymous No.12470391]

>>12469739
That defines an accumulation point.
Enumerate the rationals, and every real number would satisfy this definition.

[Anonymous No.12470996]

>>12468857
Portuguese, french, japanese and english. I understand spanish and can read pretty well, but never had a formal study in it so I don't count that. Wish I could learn german and latin too, but meh, would take too much time.

[Anonymous No.12470997]

>>12470391
Ah yes, I would need to add a "gets closer to N0 and also stays within N1 radius" bit right?
Anyway how are computations done from the definition of limit? Can you give a simple example?

[Anonymous No.12471001]

>>12469525
>en peux
Un peux*

[Anonymous No.12471011]

>>12471001
Danke schoen.

[Anonymous No.12471110]

>>12464676
Yes it does, for the delooping/classifying space [math]BG[/math]. In general for any [math]n[/math]-groupoid [math]G[/math] you have [math][X,BG]\cong H^1(X,G)[/math].
>>12466297
It [math]is[/math] harder.
>>12468857
Four.

[Anonymous No.12471163]

>>12468857
>tfw only english and spanish
I gotta step it the fug up

[Anonymous No.12471184]

>>12467021
no idea what that mu(A) thing is so I'll say this is an improper integral that diverges and call it a day
>>12467153
yea I disliked it. It involved a lot more linear algebra than I expected and I hated that class
>>12467531
I mean I took various math classes for 18 years (since I was 5 or so)
>>12468479
Honestly I only really understood calc 1,2, and diff EQ. No idea what was going on in Calc 3 or linear.
>>12468888
Chemical. We don't need to take partial diffyQ. There's a heavy focus on calculus 3 in heat/mass transfer and fluid mechanics though. Also check'd

[Anonymous No.12471276]

>>12471184
Mu(a) has to do with measure theory
Quite a fun thing to read about if you're sad about not doing math

[Anonymous No.12471295]

>>12466138
Don't let spergs like this discourage you

[Anonymous No.12471323]

>>12471184
But linear applications are so nice tho

[Anonymous No.12471524]

Anyone actually enjoy integration?

[Anonymous No.12471535]

>>12471524
you mean evaluating hard integrals?

[Anonymous No.12471550]

>>12471535
yeah or obscure ones with autistic functions and shit

[Anonymous No.12471585]

>>12468857
>Finnish
It's a dialect of Russian, so yes it is pretty complicated

[Anonymous No.12471615]

>>12471585
You do realise those two languages are not related unlike English and Russian?

[Anonymous No.12471653]

>>12464932
Instead of going for a PhD I went for the coward route and am working at a hedge fund on algorithmic trading. The pay is good and the work has been pretty light at least, but I miss interesting math.

[Anonymous No.12471757]

Third-worldnignog here. I love doing maths but graduate school here is shit and has shitty pay. So most likely I'll go be a software monkey and go to a first-world country nearby (Singapore or HK). Is it possible to balance this work lifestyle with doing pure maths or should I go take the actuarypill instead, since it also has some maths?

[Anonymous No.12471761]

How do you find a 95% confidence interval for the slope? I found the regression line to be ŷ = 5.62 – 0.75 x but I'm stuck.

[Anonymous No.12471813]

>>12470018
>will never be formalized to an extend that anybody could actually establish which theorems hold in it and which doesn't. He'll remain the arbiter of his flavor of finitism.
Axiomatization is only necessary when you're dealing with inherently vague concepts such as the completed infinite. When you're actually explain what you're talking about, when your mathematics has semantics, there's no need for axiomatization. The different schools of thought, intuitionist, formalist, predicativist all converge to one school once you actually have semantics: they all were created just because of the meaninglessness of the completed infinite.
If you really think it's so hard to "establish which theorems hold in it and which doesn't", then surely you would have an example of a theorem (and ideally a proof) whose truth value or meaning is hard to establish in an finitist framework.
I really don't think there would be any trouble in agreeing which theorems actually hold once we look at mathematics as something meaningful, whose theorems can be translated to questions about the definite states of objects in the real world.

[Anonymous No.12471961]

>>12471761
We have y = ax + b + ε, where ε ~ N(0, σ^2). This also means that y ~ N(ax +b, σ^2)
When we do regression, we find (maximum likelihood) estimators for a and b, usually denoted by a_hat and b_hat.
a_hat and b_hat both follow a normal distribution, because they're a linear combination of the sampled y_i that follow a normal.

So, you want to find a confidence interval for a normally distributed variable with Unknown variance.
This means that we need to use a student t distribution to create a confidence interval.
The estimated variance of a_hat, σ_hat(a_hat) has n-2 degrees of freedom.
(a_hat - a) / σ_hat(a_hat) ~ t_{n-2}

[Anonymous No.12471966]

>>12471961
So, it's
a_hat +- σ_hat(a_hat) * t_{n-2} (α/2)
for a 1-α confidence interval.

[Anonymous No.12471991]

>>12471615
Is there any worth in learning finnish if I'm mainly interested in math and literature?

[Anonymous No.12471992]

>>12471295
Seething midwit.

[Anonymous No.12471993]

>>12471757
In short, it's not possible, unless you're a genius.

[Anonymous No.12472040]

>>12470254
i was only going to apply to US schools but i'm considering some abroad options (really only the top few schools abroad, if you're looking at schools that aren't quite the absolute best for my research they're all in america).
overall i'm just applying to a lot of the very top schools, so i thought it was important to have a good number of apps out there since there's a pretty big dice roll component.

[Anonymous No.12472059]

>>12471991
Mathematically, not really. Väisälä's topology textbooks maybe. A lot of nice poetry, both the archaic Kalevala style and the stuff that comes to mind when someone mentions poetry, and some good literary authors, but I don't know. I would imagine the best ones have been translated to quite a lot of different languages, like for example The Egyptian by Waltari. If those are your motives, then you should have a very strong interest for it to make any sense. The archaic poetry can be quite shamanistic if presented correctly, though. https://www.youtube.com/watch?v=usDgBw8oy-U

[Anonymous No.12472077]

>>12472059
I can only speak from experience, but personally I was surprised how many great poems in Hungarian hadn't been translated to English when I looked it up some time ago. Also, I looked at some of the existing translations, and it's definitely missing a lot of beauty from the original. You can't really appreciate the true nature of a piece of art written in one language by translating its content to another, it always loses a lot of the original character, replaced by the translator's own(perhaps trying to replicate the original, but still distinct).

[Anonymous No.12472097]

>>12472077
I think it also goes the other way. A person who learned some language as an adult will never be able to appreciate poetry in that language as well as the native speaker.

[Anonymous No.12472118]

>>12472077
That is true. A lot of word play and structural things will be lost always, and definitely when transitioning between Fenno-Ugric and Indo-European languages. It's a homomorphism, but far from an isomorphism. As Hungarian is one of those FU languages, I would imagine it getting butchered quite badly as well, as would Estonian for sure. The same of course happens to other way around, too.
>>12472097
Very true. Not only will such a person miss some of the fine nuances, but also lack the contextual knowledge gathered while learning the language by living it. Of course, if you study a language (and hence the context) as a kid, you will be able to learn a lot, but still miss out on something. I just realised I accidentally made a reference to Lawvere's by mentioning language and context at the same time. Too bad (or is it?) I know nothing else about them than that it sounds like some cyberpunk theocracy's state religion.

Speaking of languages and stuff reminded me of this http://www.darkeye.net/~fredrik/fun/swedish_language.txt

[Anonymous No.12472248]

>>12472077
Translations can't indeed convey an author's writing style perfectly, but if you're really worried about that then perhaps you should indeed learn the language in which that book was originally written. In the end both readers (the ones who read the translation and the one who reads the original work) will be able to understand the main points of the book and honestly that's the part that matters the most, not that style isn't important, but for someone who doesn't want to be a writer it's the least important part of a book. Translations serve a purpose and most of the times, when done well, the only thing that they won't be able to replicate is style, even then a really good translator can mitigate any big differences in style.

[Anonymous No.12472262]

>>12464660
Where should I start if I want to learn probability theory rigorously. I quite enjoyed my bachelors classes, but some of the results are not rigorously proven.

[Anonymous No.12472277]

>>12472248
Of course, my post was mainly talking about poetry, where the particular word choices and rhythm are such a significant part of the work. I imagine when it comes to longer novels whose substance is in large part the thing they describe, and not the particular way they do it in, a skilled translated can do a mostly sufficient job, except for a relatively small number of counterexamples.
>>12472262
Going through measure theory rigorously would probably be a good start, depending on the kinds of measure theory classes you've had so far.

[Anonymous No.12472282]

>>12466297
Physics feels a lot like algebra where you're constantly pulling new definitions and "laws" from your ass. For me, I find it hard to follow sometimes.

[Anonymous No.12472292]

>>12472059
>Väisälä topologia I
It's good not gona lie.

[Anonymous No.12472302]

>>12472277
>what kind of measure theory
None, lmao. That is probably then a good place to start.

[Anonymous No.12472315]

>>12472282
But you just described Analysis.

[Anonymous No.12472332]

>>12472292
Have you read the second part? I really liked how he took the donut-coffee cup joke and turned it into how a topologist may be unable to distinguish between them, but will be able to use the fundamental group to distinguish between a coffee cup and an ordinary bun. Also, how a topologist living in a corner of a finite dimensional cube would be certain that they live in a corner, but how a topologist living in a corner of the Hilbert cube can't. No idea why, but those made me smile. Also the first several chapters were good bed reading. The problems were mostly such that you could do them in your head without having to write anything down, but still required you to think.

[Anonymous No.12472333]

>>12467107>>12467503

>Will learning about Mathematical Logic help me understand proofs in general? Can any anons redpill me about it?
yes, alot

read

A Concise Introduction to Logic
Craig DeLancey


Derek Goldrei
Propositional and
Predicate Calculus
A Model of Argument


LOGIC
The Laws of Truth
NICHOLAS J. J. SMITH

[Anonymous No.12472362]

>>12468398
>https://agrothendieck.github.io/
does not load on firefox

[Anonymous No.12472364]

>>12472315
Take that back!

[Anonymous No.12472366]

>>12472332
I haven't read topologia II. The subject itself is nicely inuitive, but the formalism grinds me. It's suprisingly difficult to write your thoughts to paper for topology.

[Anonymous No.12472367]

>>12470018
he has a book for teaching maths and the reviews are nice to him

[Anonymous No.12472368]

>>12467607
Is this recent? If so, I'm very glad to see Maimon posting again

>>12468706
>>12468335
>>12468523
Hi fellas I'm a year out from being in your position, any golden advice to share? Also.... good luck!
>>12468857
English Russian German, I can sort of still read Latin

[Anonymous No.12472378]

Question: is it meaningful to speak of Natural numbers as a unique natural completed infinite?
Suggestion for a way to find an answer to this question:
Do one of the two
1. (Program in favor of finitism) Try to formulate a meaningless undecidable arithmetic proposition with a convincing argument that it has no natural truth value.
As formulated, nobody has convincingly done this yet. Godel and subsequent logicians have found undecidable arithmetic propositions but so far all of them have had natural truth values with a convincing argument for their truth from an infinitist framework, and from an infinitist framework they make a more convincing case for infinitist Platonism rather than finitism because they go against viewing arithmetic as merely shuffling of finite formulas, provided you believe in meaningfulness of large numbers.
2. (Program in favor of infinitism) Try and find a convincing argument (possible assuming infinitist framework) that point 1 cannot be done.

Thoughts?

[Anonymous No.12472380]

>>12472368
Get all the necessary elements together early. Hopefully you have done some research by now, if not, then you really need to get some kind of experience between now and when you apply. Also, think about the 3 people who will write GOOD recommendations for you when the time comes. Lastly, think about what the narrative of your academic career is and why you want to go to grad school so you will have something to say in your personal statement.

[Anonymous No.12472387]

>>12472380
>research
I'm not sure I see myself landing something like this any time soon, what with the COVID and all. Is this as much of a prerequisite for an M.S. ?

[Anonymous No.12472393]

>>12472366
I really recommend you do, but I think he is going against the usual conventions with this separation axioms a bit in that, so beware! If I remember correctly, his T3 is what most authors would call regular and vice versa (and same for T4 and normal). I agree with the intuition vs writing thing. I remember how it took me ages to write the proof that the suspension of a sphere is homeomorphic to the sphere one dimension higher despite it being pretty obvious after just a few minutes of thinking. It's just so easy to get intimidated by all the scary sounding stuff, but then you find a gap in the seemingly impenetrable wall and boom! Which year are you?

[Anonymous No.12472397]

>>12472262
What do you mean rigorously?
I wouldn't recommend measure theory cause it's pointless autism.

[Anonymous No.12472398]

>>12472362
Then stop using shitty browsers.

[Anonymous No.12472410]

>>12472393
Currently third year bachelors. I think I'll do topology only during masters though.

[Anonymous No.12472412]

>>12472397
Mostly with stuff like probability spaces and the like. I don't remember any particular examples of unproven theorems from less advanced courses, but they do come along quite often.

[Anonymous No.12472416]

>>12472368
Yes, Ron is active a lot on YouTube. Especially chess videos.

[Anonymous No.12472421]

>>12472397
What approach would you suggest other than measure theory? Personally I felt a marked improvement in my intuition about random variables and the like after taking a measure theory course, not into such depth as operator spaces but the basics at least really helped, in my experience.

[Anonymous No.12472436]

>>12472410
Topology and algebra, those are my recommendations for master stuff. Algebraic topology is pretty good stuff if you are interested in abstract nonsense.

[Anonymous No.12472438]

>>12472387
I would say for an M.S. that research experience is not as important. However with maths you don’t have to be in person to do research, maybe something as small as an independent study with a professor who you enjoy talking to and working with.

[Anonymous No.12472486]

>>12472438
Do you think it's unreasonable to cold-email a prof whose field you are interested and somewhat literate in, asking to do an independent study on it? Thanks for your help thus far, by the way.

[Anonymous No.12472522]

>>12472436
Hate to disapoint the donut lady but I'm more of an stats guy. Algebra feels too abstract.

[Anonymous No.12472530]

>>12472486
what is a cold-email?

[Anonymous No.12472537]

>>12472530
Emailing someone whom you have never met in person

[Anonymous No.12472540]

>>12464811
>4x+6x=9x(2x)2+(2x)(3x)=(3x)2 let a=2x,b=3x then a2+ab=b2,a,b∈R>0a2+ab−b2=(a+ib)2−2abi+ab=(a+ib)2−ab(2i−1)=(a+ib)2−ab(5√ei(π−tan−12))⋯(1)=(a+ib)2−(ab5√−−−−−√eitan−1φ)2=X=0, where φ=1+5√2Re(X)=a2−b2−ab5√cos2(tan−1φ)+ab5√sin2(tan−1φ)⋯(2)=a2−b2−5√ab11((4−5√)−(7−5√))=a2+35√11ab−b2=0∴a2+35√4ab=b2∴4x+6x=9x⟺4x+(35√11)6x=9x∴x≈1.1868⟺x≈0.7407(⊥)((1):tan−122=tan−1φ−1,tan−1φ+tan−1φ−1,=π2)((2):cos2(tan−1φ)=1φ2+1=4−5√11,sin2(tan−1φ)=φ2φ2+1=7−5√11)

[Anonymous No.12472541]

>>12472537
ah okay, thanks

[Anonymous No.12472575]

>>12472486
There is definitely no harm in doing that. Of course, their chance of replying is higher if they actually know you. Another thing you could consider doing is if someone you do know works in the same general area, say algebra, then you could ask for an introduction to get the ball rolling. Right now is a pretty busy time for most professors so don’t take it personally if you don’t get an immediate response. Just follow up with them politely after a week or so.

[Anonymous No.12472580]

>>12472575
Thank you man, really needed someone to sanity check me on this.

[Anonymous No.12472586]

>>12472580
No problem. One last piece of advice, make sure you are specific about what exactly you want to work on, maybe even suggesting a reference text or paper that you would like to understand better. It makes you seem more serious. Also, make sure you ask about setting up a time to meet on Zoom or whatever online conference software you use.

[Anonymous No.12472602]

>>12472522
Yeah I understand what you mean. Different tastes, not everybody wants raisins in their liver box and so on. Whatever your path has coming to you, good luck with that!

[Anonymous No.12472657]

>>12466297
im in a physics masters and math is 100 times harder than what we do lol

[Anonymous No.12472660]

>>12472602
>not everybody wants raisins in their liver box

[Anonymous No.12472737]

>>12472660
>Not eating liver box

[Anonymous No.12472886]

>>12472660
If I wasn't a vegetarian, I'd learn how to make this and kill myself with whatever negative stuff there was in liver that you can basically overdose on. https://en.wikipedia.org/wiki/Maksalaatikko

[Anonymous No.12472937]

>>12472886
I like liver, but I usually eat it fried like beef.

[Anonymous No.12473054]

>International seminar for young researchers "Algebraic, combinatorial and toric topology"
>(December 17–18, 2020, online)
http://www.mathnet.ru/php/conference.phtml?confid=1885&option_lang=eng
Moscow time GMT+3!
>>12472937
I'm not sure if I've ever done that.

[Anonymous No.12473095]

>>12464660
>Taking complex analysis (for math majors) next semester
Can someone pls suggest some good textbooks for a more rigorous focus on the subject?
I searched online and say a reddit thread with a bunch of people suggesting visual complex analysis by Needham but that book seems to be more for physicists or engineers than for mathematicians.
Keep in mind that in order to be able to take this class you must have taken and passed 3 (12 week) classes into real analysis already.

[Anonymous No.12473170]

>>12473095
My university uses Complex Variables by Stephen Fisher. I have see other anons recommend Complex Analysis by Stein and Shakarchi.

[Anonymous No.12473179]

>>12464660
I AM DONE TRYING TO LEARN THIS RETARDED SUBJECT
I SUCKED IN HIGH SCHOOL, I TRIED FOR THREE (IN WORDS: THREEEEE) YEARS TO GET BETTER BUT I KEEP GETTING FILTERED BY BASIC THINGS
REEEEEEEEEEEEEEEE

[Anonymous No.12473214]

>>12473179
>I KEEP GETTING FILTERED BY BASIC THINGS
Like what?

[Anonymous No.12473222]

>>12473095
Ahlfors is a classic. Also Gamelin is quite nice too since there is so much material that he covers (it may make a good supplement to Ahlfors).

[Anonymous No.12473277]

>>12473214
>Like what?
Like basic stochastics (binomial coefficients and such)
My entire foundation is shakey and I always forget what I """learned"""

[Anonymous No.12473347]

>>12473214
>>12473277
There was a question on my last exam. It's literally high school tier, but I think I still don't know the answer:

Twelve horses, numbered 1-12, run on a race track. What is the probability that horse number 2 passes the finish line first, followed by horse number 3?

So, I think that's really asking what the probability of two consecutively numbered horses crossing the finish line in order is, right?

So it would really be a ballot box model described by
[math] \frac{n!}{k!(n - k)!} [/math]
right?

So that would give us

[math] \frac{12!}{2!(12 - 2)!} [/math]

which is 66. So the answer found be 1/66? That seems way too low.

I am completely retarded

[Anonymous No.12473363]

Hello /mg/. It's me your friendly schizo. I'm on a lot of legal stimulants. Does anyone want to play programming games with me?

[Anonymous No.12473378]

>>12473347
It should be
(10)!/(12)! = 1/(11*12)=1/132

[Anonymous No.12473386]

>>12473347
I'm retarded. It would be described by
[math] \frac{n!}{(n-k)!} [/math]
since the order is important, no?
So it would be 1/132?

[Anonymous No.12473395]

>>12473386
>>12473378
>>12473347
>>12473277
>>12473179
WHY CAN I NEVER DO THIS CORRECTLY THE FIRST TIME AROUND THIS IS LITERALLY HIGH SCHOOL TIER MATHS
FUCK THIS SHIT REEEEEEEE

[Anonymous No.12473688]

>>12473095
Ahlfors for homography, Remmert if you like a good book with historical segments, Lang's Complex analysis is also nice, Conway, Functions of one complex variable,

[Anonymous No.12473873]

>>12473170
>>12473222
>>12473688
Thank you very much anons. I'll check out all of your suggestions

[Anonymous No.12474139]

anyone wanna go over folland and allufi with me during winter break?

[Anonymous No.12474151]

>>12474139
it'll mostly be just solving problems btw. Won't really discuss the material as I've seen it before.

[Anonymous No.12474177]

I think I could make a cute girl. I used some sort of face AI app to get a painting version of me and in it I look very much like a cute woman.

[Anonymous No.12474210]

>>12472540
Shut up faggot
This happens every time someone posts anything that isn't algebra or topology

[Anonymous No.12474424]

>>12473054
It's good and it's easy.

[Anonymous No.12474431]

Pls help me /sci/, I'm retarded.

How do you find the largest partition of a set, given certain relations? By largest partition I mean the partition with most sets. With no restrictions this would be trivial, e.g. [1 2 3 4 5 6 7] gives [1] [2] [3] [4] [5] [6] [7]. But say you had relations like

1
2 ~ 4
3
4 ~ 6 7
5
6 ~ 4
7 ~ 4

So the partition with 2 must also contain 4, and 4 must also have 6 and 7, so the largest partition is [1] [2 4 6 7] [3] [5]. Is there an algorithm that can solve this without needing to loop n times or reach huge recursion depths (e.g. 1~2, 2~3, 3~4... would lead to a shitload of recursion)? Is this even a studied problem, and if so what do I need to search to read up on it? Is there a really simple algorithm I can't see because I'm retarded? Does it help if you can assume the given relations are symmetrical (but not transitive)?

[Anonymous No.12474551]

>>12474424
Not denying that possibility. I just don't eat meat myself, but maybe I could make it for someone else some day, perhaps. Thanks for the idea. That liver box is really worth trying, though. By the way, I don't know if you do Kähler stuff, but this would be live in roughly 5 hours.

[Anonymous No.12474553]

>>12474551
DID I JUST SERIOUSLY FORGET THE LINK? HAHAHA http://www.mathnet.ru/php/presentation.phtml?option_lang=eng&presentid=29225

[Anonymous No.12474569]

>>12474431
just build a tree

[Anonymous No.12474582]

Do you guys think [math] i A^{ \mu } \partial_{ \mu } - m [/math] admits a valid green's function? Trying to see what happens if I make an electron-like scalar field along some "flow" [math] A^{ \mu }[/math] (which I will assume is constant at this point. Took a fourier transform and arrived at [math] D_F( x - y ) = \int \frac{ d^4 p } { ( 2 \pi )^4 } \frac{ e^{ - i p ( x - y ) } }{ A_{ \mu } p^{ \mu } + i m } [/math]

[math] = \frac{ x_0 - y_0 }{ A_0 } e^{ -m ( x_0 - y_0 ) / A_0 } \int \frac{ d^3 p }{ ( 2 \pi )^3 } \left\{ e^{ -i \mathbf{ p } \cdot \left( \mathbf{ A } ( x_0 - y_0 ) / A_0 - ( \mathbf{ x } - \mathbf{ y } ) \right) } \right\} [/math]

Seems bad, not really sure if it is Lorentz invariant (or has some easy lorentz transformation property), or how I can get the final integrals to converge to something meaningful

[Anonymous No.12474604]

>>12474551
>>12474553
I'm planning on being asleep around that time, but I'll watch it tomorrow, thanks for the link.

[Anonymous No.12474682]

>>12474177
Post body.

[Anonymous No.12475087]

>>12466776
As a CS student I felt this.
Differential Equations were so fun for me and it’s the last topic we see for math.

[Anonymous No.12475158]

I really like learning new math topics and the skills/techniques it provides, but I HATE proofs. I know it's cringe normie talk but someone reassure me that it's okay to learn the high-level concepts, definitions, theorems and how to apply them while simultaneously neglecting all proof writing.

[Anonymous No.12475176]

>>12475087
>>12466776

>ode class for engineers
>fun
How do you sickos do it

[Anonymous No.12475202]

sorry for the dumb question but are the -1 / 1 endpoints exclusive or inclusive with the sinus

[Anonymous No.12475226]

>>12475158
Well, if you don't have any intention of being a mathematician and are just studying recreationally that's ok. Otherwise, it's ok for when you're trying to get the big picture of a topic but at some point you absolutely need to be willing to go through the proofs of what you read, understand them, and use them as a springboard for your own.

>>12475202
If you are talking about the range of f(x) = sin x then inclusive

[Anonymous No.12475234]

I have less than 2 days to decide where to go for PhD and I don't know what to do.

Relevant: My insterests are Number Theory (mainly algebraic) > Algebra (mainly commutative) > Analysis (mainly non-geometric) ≥ Combinatorics > Geometry (mainly non-differential).

I have two main choices.
[math]\bullet[/math] One is the best institute in my country. (Not just in my country, actually.) There are a few professors that work on areas that overlap with number theory, in particular 3 that work with algebraic geometry (which could me introduce to concepts of diophantine geometry). But one of them is too much of a geometer, the other is nearly dead and idk if would accept any more students, and the last one if overflown with PhD students. There's also a professor who works with automorphic forms, but it's way more analytical and geometric than arithmetic.
[math]\bullet[/math] Second, it's an uni close to second best (if not 2nd) in math countrywise. A professor I personally know (talked a bit more with him than any other) from there made me a PhD project proposal, with potentially a better scholarship. I have a good relationship with him and he's probably gonna have more disposable time than the others from the first option. Plus, he's a worldly known in his area, very prolific. But he works with a non-commutative area in algebra that employs a lot of combinatorics that I don't know much about.


I've already accepted that I have to get off the number theory boat (at least for a while), but I need to maximize my enthusiasm for whatever I'm going to study, while also taking into account future prospects etc.
I'm not a genius, so I can't just try to study whatever the fuck I most like alone if I want to actually proceed.

Wtf do I do, /mg/? I'm really lost.

[Anonymous No.12475273]

>>12472398
This. Install Brave

[Anonymous No.12475309]

>>12475234
number 2, having a supervisor you dig is mad important for passion. Also, imo it's better to have a prof big in his area rather than one at a big school, particularly the third guy with too many students, it's way better for your own development to study under a guy who can actually give you his time. Don't worry about not knowing much about the advanced combinatorics, that's why you're studying! (for real, the supervisor is there for questions and discussions, and if you're really lost he will recommend you PLENTY of reading material) Good luck!

[Anonymous No.12475325]

>>12471550
i do

[Anonymous No.12475330]

>>12474582
bump

[Anonymous No.12475333]

anons wish me luck calc II w/ introduction to vectors final tomorrow 40% of my grade

[Anonymous No.12475335]

>>12475333
>using "w/" instead of "with"
Not gonna make it

[Anonymous No.12475338]

>>12475335
anon i cannot be assed to type right now it's 3am i'm having an existential crisis

[Anonymous No.12475346]

Can someone shed light on representation theory? Ok so basically you have abstract objects from group theory and other abstract fields but you can write them down as a specific matrix so its easy to do practical calculations. The problem is you can choose the size of the matrix.. It can be 3x3, 4x4, 50x50, all the way to infinite, and all of them would be representatives of tge original abstract object. For instance i can represent a 3D rotation with a 3x3 matrix but could also with an 800x800 matrix if i feel like it. The problem is that alm these different representations have "extra properties" that have nothing to do with the original abstract object. For instance they have different eigenvalues, so these representations appear to have additional structures attached. What is the meaning of this? To what level can we say that a matrix representation of an abstract object "represents" the object?

[Anonymous No.12475357]

>>12475338
I graduated 11 years ago. The ride never ends.

[Anonymous No.12475378]

>>12475309
Thanks for your take, anon.
About the third guy you mentioned: He's also big in his area (one of the two most influential in algebraic geometry in my country). I have a good relationship with him too, but I think the 2nd option prof is closer to me. But having a lot of students and organizing a unch of events really takes time.
The 2nd option's professor also has a bunch of things to do and some students. Right now he has one PhD, one post-doc, two undergrads and two masters. I don't know how much time he's going to have for me, but I'd still bet more than that third professor.
Also, it's not just combinatorics I don't know much about, but also non-commutative algebra. It's more that I don't know how the experience is going to be, I can only hope I'll like it since I don't dislike combinatorics and algebra in general.

[Anonymous No.12475462]

>>12475346
One can approach the subject from two directions. For simplicity, let's say we have a finite group [math]G[/math] and some commutative ring (unital) [math]R[/math]. We can then think of all the groups of square matrices with non-zero determinants and with entries in [math]R[/math], denote those by [math]GL_n(R)[/math], where the subscript tells you the dimension. If the dimension is too small, then there will be non-trivial relations (or the homomorphism [math]\rho \colon G \to GL_n(R)[/math] will have a non-trivial kernel, and if the dimension is too big, it it will provide no information we did not already have. Let's simplify even more and assume our ring [math]R[/math] is a field [math]k[/math]. Then [math]GL_n(k) = \text{Aut}(k^n)[/math], so actually we obtain an action of the group on the n-dimensional vector space over the field of choice. We may then ask what is the minimal dimension such that the kernel is trivial, and that for example will give us an invariant that can be used to distinguish between groups.

The other direction is that we start by constructing the group algebra [math]RG[/math] and then the modules over this group algebra are obtained like above. Take the free [math]R[/math]-module [math]R^n[/math]. Its automorphisms are the nxn-matrices with non-zero determinants, so map your group into that, and then use the projections [math]R^\mathscr{J} \to M[/math] to obtain all the possible actions of [math]G[/math] on [math]R[/math]-modules. Again using a field, we have the actions of our group on the vector spaces. Actually, this time we don't think about the action itself, but we think of it as the scalar multiplication of [math]kG[/math] (as [math]R=k[/math] for simplicity again). Then one can use all sorts of ring theoretical tricks to compare different groups, like for example ask what are the simple or indecomposable modules like, and so on.

Two corresponding ways to answer the same questions with different tools. Hope this helps.

[Anonymous No.12475488]

>>12475462
>simple or indecomposable modules
And to add a bit, this isn't as stupid as it sounds. It would be completely idiotic to ask what are the indecomposable or simple vector spaces, but these are those, these are modules over [math]kG[/math], so they need not coincide.

[Anonymous No.12475497]

>>12475462
Thanks for your effort-post but it is way above my level. Can you recommend a book on representation theory?
Lets talk about terminology. When you say modules are you referring to different representations of the same group but according to the dimension? Like 3x3 matrix are a module od dimension 3, 7x7 matrix representation (of the same group) are a module of dimension 7?
Also did you say there is a specific module of some dimension with kernel=0 and lower dimension is a subspace and higher dimension doesn't have new information? What is the meaning of this specific representation? (Module is the right term?)
My motivation comes from quantum mechanics. Its said that different representations are associated to different physical particles, but i assumed a representation was just "some way" to write down a group or algebra element in a concrete way.
Post is to diffuse, plz recommend book

[Anonymous No.12475512]

>>12475497
Just quickly reading on wiki they talk about "modules" being a new concept, a generalization of vector spaces.
I studied linear algebra, vector spaces and all that up to some depth level. Are modules are new structure worthy of study?

[Anonymous No.12475542]

>>12475512
Yes, modules bring a lot more to the table than just vector spaces, like rings do so compared to just fields.
But you probably don't need to worry much about them if you just want to understand representation theory. The most basic stuff (like those isomorphism theorems) are similar to vector space stuff.

[Anonymous No.12475552]

>never do proofs by contraposition
>always just assume A and not B and then show not A

[Anonymous No.12475553]

Does anyone know the closed form for [math]\int^1_{-1}P_n(x)e^{ax}dx[/math]
where [math]P_n(x)[/math] is the n-th Legendre polynomial?
When [math]n=0[/math] it's obvious, just [math]\frac{2\sinh a}{a}[/math]
but for [math]n>0[/math] I can't decide whether it's [math]\sqrt{\frac{2\pi}{a}}\frac{I_{n-\frac12}(a)}{2n}[/math] where [math]I_\nu(z)[/math] is the modified Bessel function, or whether it's [math]\sqrt{\frac{2\pi}{a}}I_{n-\frac12}(a)\tanh a[/math] which is what I ended up with after integrating by parts and solving the recurrence relation.
I think it's probably the first one but maybe someone else knows better. Trying two derivations and getting two answers got me confused.

[Anonymous No.12475558]

>>12475497
>Can you recommend a book on representation theory
Not really, sorry. I approach it from the group algebra direction pretty much always, so I can't really recommend anything for sure. A book I sometimes use for reference is Burrow - Representation Theory of Finite Groups, and it is old but good.
>Like 3x3 matrix are a module od dimension 3, 7x7 matrix representation (of the same group) are a module of dimension 7?
I mean the number of rows (and/or columns, square matrices). Let's say we have the field of just 2 elements, 0 and 1. How many 2x2 matrices can we have? 16 is the total, and then we need to have non-zero determinants, which will reduce that to something like 4(ish) possibilities. If we would now try to send the elements from the cyclic group of 16 elements to those matrices, that would necessarily force distinct elements to be sent to the same matrix, and so on.
>Also did you say there is a specific module of some dimension with kernel=0 and lower dimension is a subspace and higher dimension doesn't have new information?
Let's just think of them as vector spaces. If we can get an injection into the automorphisms of an n-dimensional space from our group, then there is nothing new to be learned by mapping our group to the automorphisms of an (n+m)-dimensional space for any m>0, as the image of will then be those matrices in which the nxn top left part is the same, the rest of the main diagonal are 1's and all the other entries 0. That's what I meant. If we get rid of the redundant part, then (I think) this will give the minimal faithful representation of your group, but I'm not too familiar with this matrix formalism to say for sure.
>representation was just "some way" to write down a group or algebra element in a concrete way.
Yes. Any group can be turned more concrete by embedding it into a symmetric group. Similarly, these representations can be used to turn an arbitrary group into matrices.

Really hitting the character limit lately.

[Anonymous No.12475568]

>>12475497
https://www.youtube.com/watch?v=9rDzaKASMTM&list=PL57457844458A5A1F
If you want a buff guy to explain stuff to you, I recommend him.

[Anonymous No.12475605]

Are there multiple assholes flooding this general with anime or is it one mega-faggot?

[Anonymous No.12475619]

>>12475605

[Anonymous No.12475629]

>>12475619
Yeah seems to be you. Are you not ashamed of yourself?

[Anonymous No.12475637]

>>12475605
I think there are multiple anime posters, but just one touhou poster. You can tell it's him if the girl has a silly hat or a frilly dress as seen in >>12475619

[Anonymous No.12475646]

>>12475234
>But he works with a non-commutative area in algebra that employs a lot of combinatorics that I don't know much about.
Sheesh, that second option was too good to be true, there's always a catch in the end, go for the first one.

[Anonymous No.12475660]

>>12475605
There are around 3 or 4 but all of them know a lot of math and help others a lot and are probably more advanced than you.

[Anonymous No.12475664]

>>12475158
it's okay if you do maths in dilettante

[Anonymous No.12475666]

>>12475234
>>12475605
At least one of them answered me.

HELP ME
THIS DILEMMA HURTS

[Anonymous No.12475667]

>>12475637
Your deductive skills are shit, you can tell that there's at least three just from
>>12468912
>>12470996
>>12471110

[Anonymous No.12475668]

>>12475158
Think of proofs as explanations of what's going on.
>learn the high-level concepts, definitions, theorems and how to apply them while simultaneously neglecting all proof writing.
You won't understand the concepts without also understanding the proofs.
What you're describing is analogous to just reading the headlines in news articles, and using this extremely limited information to delude yourself into understanding what's going on.

[Anonymous No.12475670]

>>12475234
>>Wtf do I do, /mg/? I'm really lost.
if you are an autonomous genius, then 1., otherwise 2.
having a good relationship with the phd supervisor is more important than the topic if you cant hack it alone. plus here the topic is close to what you want.

also check which uni has the most conferences about what you like, or at least pays the most to go to conferences.

finally, start managing your bibliography right now with mendeley and watch conferences on youtube each day , or at least each week

[Anonymous No.12475672]

>>12475646
haha what triggers your allergy more, non-commutative stuff or combinatorics?

[Anonymous No.12475677]

>>12475667
He is schizophrenic

[Anonymous No.12475681]

>>12475660
they're still pedos

[Anonymous No.12475683]

>>12475234
There are two main things to consider. Firstly that the best institute will have a better academic environment, and being exposed to that kind of cross fertilisation is very beneficial to you.
Secondly, the relationship with the supervisor is very important. Depending on your relationship, and his quality, that alone could outweigh any level of institutional esteem.
But in the end I'd say the big thing is you have to be a bit unrealistic with yourself here. Go for what you aspire to become, not what you think you realistically can do. You'll only get this opportunity once, and you will regret it if you don't reach for your ambitions. If there's one choice that really gets you excited, go for that one.

[Anonymous No.12475689]

>>12475568
Thanks doc, will watch

[Anonymous No.12475695]

Has /mg/ iterated their dilators yet?

[Anonymous No.12475767]

>>12475672
Combinatorics obviously, at least non-commutative algebra is still algebra and therefore doable.

[Anonymous No.12475834]

>>12475552
But this doesn't work anon

>>12475695
>nice flower

[Anonymous No.12475902]

>>12475553
Strange that this integral is not given in Gradshteyn and Ryzhik despite having such a simple form.

[Anonymous No.12475923]

>>12475553
The laplace transform of the Legendre polynomials is stated here https://mathworld.wolfram.com/LegendrePolynomial.html
At least in the case [math]n[/math] it should be possible to use this to find what you're looking for

[Anonymous No.12475945]

>>12475670
First two points awards option 2. Second to last phrase: Option 1 has more NT stuff etc; and I can't decide which option is better for funding academic travels. 2x1, so that would be option 2...

>>12475767
He's actually an IMO medalist, so it's kind of expected for him to like combinatorial trickery. I met him due to olympiads too, but I've always been mediocre at them, so I have a bit of fear of not being able pull out these sort of tricks. It's just that there aren't many other olympics around him, I think.

>>12475683
>You'll only get this opportunity once, and you will regret it if you don't reach for your ambitions.
God dammit, anon. My heart is beating and my mind is fucked.

[Anonymous No.12475978]

>>12475945
Don't fear the combinatorics too much.

[Anonymous No.12476160]

>>12475670
Can you redpill me on mendeley? Never heard of it.

[Anonymous No.12476169]

Did he ever find his mushrooms? How many?Mathematically speaking.

[Anonymous No.12476172]

i love probability but i fucking hate probability tests. questions are always written in the most nonsensical, cryptic indecipherable prose possible just to fuck with students. not to mention the questions based on board games or very arbitrary events that no one has ever experienced, or other half page long questions.
i got a fucking C just because i misunderstood half of the fucking questions when i literally could have solved them all easily

[Anonymous No.12476200]

>>12476169
it's not autistic, it's a useful hobby that many people might study in university for years.
why do westerneroids want to shame people whenever its possible? the guy likes to walk in nature and collect fungi maybe to plant it or to eat it. it's fun, calming, pure, innocent, ascetic experience unlike being a math celeb.

[Anonymous No.12476221]

>>12476160
I can give you the rundown if you ask properly instead of using /pol/ terminology.

[Anonymous No.12476231]

>>12476200
Perelman did that? What's this mushroom story all about? First time hearing it.

[Anonymous No.12476244]

>>12476231
he didn't study mycology or anything. a reporter once called him for an interview and he said something like "You are disturbing me. I am picking mushrooms".
foraging the forest in free time is very common in rural europe even in urban europe

[Anonymous No.12476252]

>>12476244

Reminds of "Don't disturb my circles!" by Archimedes before being killed.

[Anonymous No.12476268]

>>12476244
based

[Anonymous No.12476279]

Why does ln(x) cancel e?

[Anonymous No.12476304]

>>12476279
do you mean why ln(e^x) = x ?

[Anonymous No.12476306]

>>12476279
Because he found out e used to post racist jokes on twitter.
Actually it's just that logarithms are the inverse of exponential functions, and ln(x) is the inverse of e^x.

[Anonymous No.12476327]

Will learning Linear Algebra make Calculus easier?

[Anonymous No.12476342]

Why is he such an autist, /sci/?

[Anonymous No.12476367]

>>12474551
>>12474553
I think they goofed the recording somehow.
The link in the page does lead to a recording, but it starts at Abramyan's presentation (the third one in the chronogram) and finishes at Gorodkov's (the fifth), after which the chronogram plans a four hour pause.
Maybe they'll figure it out soon and upload the whole thing.

[Anonymous No.12476378]

>>12475497
Serre's Linear Representation of Finite Groups

[Anonymous No.12476382]

>>12476327
I swear I see this question every thread. Is it you every single time?

Anyway the answer is yes, but only because, in general, the more you study math the easier it gets to study math.

[Anonymous No.12476401]

>>12476327
linear algebra is absolutely necessary for a thorough understanding of calculus, because its whole point is reducing non-linear problems to linear ones
but it won't really help you with solving calculus problems, if that's what you're asking

[Anonymous No.12476418]

How can you infinitely derive a function? Aren't you eventually going to end up at f(x) = 0?

[Anonymous No.12476430]

>>12476418
No, consider the trig functions for example.

[Anonymous No.12476431]

>>12476418
>derive
it's "differentiate"

[Anonymous No.12476483]

>>12476160
mendeley is a little software to manage all the pdf you save from arxiv. it's important to get bibliography right and as soon as possible, instead of putting it off to the last year of the phd

there is an option in mendeley to NOT share your bib. i think it's with shift+D, then find the option.

[Anonymous No.12476485]

>>12476418
There's even a function that you can differentiate infinitely often and it will stay the same! Exercise for you: How would the slope field of such a function look like? What properties can you derive?

[Anonymous No.12476496]

>>12476252
Full story?

[Anonymous No.12476499]

>>12476221
gee it's just a memetic expression at this point...
Ok mathpill me on mendeley then, plz

[Anonymous No.12476500]

>>12476306
It's by definition then?

[Anonymous No.12476503]

>>12476367
Like you actually know shit about Kähler Manifolds, you're not even an algebraic topologists.

[Anonymous No.12476506]

>>12476503
>Kahler manifolds
>algebraic topology

[Anonymous No.12476515]

>>12475945
You have to build a network, or at the very least know which people matter in what you like and-or study in order to get a postdoc. But to get a postdoc , first you need a good thesis, even if the topic is not the one directly connected to the postdoc. There really should be between 5 and 30 people in the world you should know the names and where they work.

I would take 2. and make myself known to the people in 1. and 2. Especially during of conferences involving people in 1.
So thesis with 2. and postdoc with 1.

Try to get in tough with the emeritus professor and tell him what you work on and what you like and at some asking him if knows some postdoc positions.

[Anonymous No.12476518]

>>12476485
this is wrong, the derivative of an even function is odd. Unless you are on some weird space or it is the zero function, which I guess is both even and odd maybe?

[Anonymous No.12476525]

>>12476515
actually you can talk about who will be the jury on your presentation. If you manage to make you supervisor agree that some people from 1. can be your jury, it's complete win on your side. The more famous your jury is ,the better for your career.

[Anonymous No.12476530]

>>12476506
Algebraic topology is a tool for complex manifolds, imbecile.

[Anonymous No.12476539]

>>12476536

>>12476536

>>12476536

[Anonymous No.12476547]

>>12476503
Even if, hypothetically, I didn't know jack about Kahler geometry, judging from how Abramyan explains what the fuck are cohomology operations (it's mostly a topology seminar, so the bar for geometry knowledge is most likely even lower), I could probably still watch it.

[Anonymous No.12476551]

>>12476530
that doesn't imply that one needs to know algebraic topology to know kahler manifolds

[Anonymous No.12476552]

>>12476547
Timestamp for that claim is 14 minutes, btw.

[Anonymous No.12476574]

>>12476518
Anon, I think there is quite a difference between "theres even a function" and "theres an even function"...

[Anonymous No.12476598]

>>12476367
Fug... Maybe, hopefully. Or maybe it will be like in the UK where pages are never updated, but some pages just get deleted and then you have a bunch of dead links leading to nowhere. Were the other talks good?

[Anonymous No.12476794]

>>12475462
>groups of square matrices with non-zero determinants
.::.:..:...:::.:....:..:....:.....:.:....:::::::::::::..

[Anonymous No.12476862]

>>12476525
a thesis in maths is proving at least 1 big theorem, so try to make this theorem relevant for the people in 1.
Or you can explore first the non-commutative case of whatever you do, and then do the commutative case and present it to the people in 1.

[Anonymous No.12476903]

>>12474582
nvm mein duden.
Woke up after an okay night's sleep and saw the delta function definition sitting right there. Weird green's function though. Not too sure about interpretation.

[Anonymous No.12477441]

>>12476500
Depends what you mean by that
If you have some calc text check out how log is defined

[Anonymous No.12477800]

>>12476574
oh haha dyslexia moment

[Anonymous No.12478709]

>>12467607
>youre really pissing me off here