/sci/ - Science & Math

>>8962385
I am trying to understand the solution to this exercise.

I think I get it all the way until the end. How can you guarantee that you can choose such an [math] x_0 [/math]? Can you even guarantee that the o(1) term will be smaller than b-a?

That said, if someone could explain the entire argument that would be good too because... maybe the reason I don't get that final part is because I am not truly getting the parts before.

>>8962412
>Can you even guarantee that the o(1) term will be smaller than b-a?
doesn't that follow immediately from the definition of little o? i.e. for all epsilon>0 the o(1) term is eventually bounded above in absolute value by epsilon, so you can just take epsilon= (b-a)/2

>>8962418
I didn't... realize. Little o was defined in this very chapter and I guess I haven't had time to digest.

But I think I get it. If f(x) = o(1) then that means that the limit as x approaches infinity of f(x)/1 equals 0. And therefore the limit as x approaches infinity of f(x) is 0. And that means that functions in the o(1) class get arbitrarily small.

Holy shit fuck. This was trivial. I can finally see

there is a conformal map from the unit disk, D(0,1), to the puncture unit disk, D(0,1)\{0}

you guys won't find one though

>>8962439
I'll puncture your unit with my disk if you keep on with that cheek

>>8962385
I have found something quite remarkable regarding CFT and TQFT that basically confirms my suspicion from last thread.
Will post details after I'm home.

Be honest, do you use "nootropics"?

>>8962452
do energy drinks count?

>>8962452
Does coffee count?

>>8962452
Does semen count?

>>8962465

engineer detected, lol.

>>8962458
>>8962463
>>8962465
xDDDDDDDDDDDD
oh wait that was really really epic and funny, let me break out my surplus supply of d's
xDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD

>ywn never play chess against Urschel
>ywn never prove theorems with Urschel
>ywn never throw football around with Urschel
just kill me senpai

>>8962458
>>8962463
No, I mean stronger stuff.

>>8962497
What's wrong with this thing on the image?

>>8962524
2 energy drinks?

I know it's unknown if there is a bijection from [math]\mathbb{Q} \times \mathbb{Q}[/math] to [math]\mathbb{Q}[/math], are there other sets like this? Where we don't know if theres a bijection from its cartesian square to itself?

>>8962542
>I know it's unknown if there is a bijection from Q×Q to Q
wrong, both are countably infinite so there's a bijection between them.

>are there other sets like this? Where we don't know if theres a bijection from its cartesian square to itself?
i think for any infinite set that the cardinality of the square is the same as the cardinality of itself, so there's a bijection. it obviously breaks down for finite sets

>>8962547
Sorry, I meant where we don't know what the bijection is

>>8962548
it shouldn't too hard to get one from Q to Q x Q , just find one from Q to N and one from N to Q x Q and compose them

>>8962497
I call fake. Someone is ghostwriting his articles.

>>8962542
The cartesian product conserves cardinality. (For infinite sets.)

>>8962548
Sorry, any finite product of infinite sets has the same cardinality as the set with the highest cardinality in the product.

[math] #\mathbb{Q}^n = #\mathbb{Q} = {\aleph}_{0} [/math]
[math] #(\mathbb{C}^k \times \mathbb{R}^l \times \mathbb{Q}^m \times \mathbb{N}^n) = #\mathbb{R} = c [/math]

>>8962565
Yup, I can confirm this.

Im taking calc-1 and it took me a full day to understand the ε, δ concept of a limit. Am I retarded?

>>8962788
No. It's a difficult definition if you are not used to pure mathematics. You slowly get better at understanding things as you keep on learning. Keep at it!

>>8962542
>>8962547
Brings to mind a very interesting exercise:
>Is Q isomorphic as a group to the direct product of two non-trivial groups? Why or why not?

>>8962548
As far as I know there aren't any examples of sets that are known to have the same cardinality but no specific bijection is known.

Even if you have to use the Schroeder-Bernstein theorem, the proof of it is constructive so really you could describe the bijection if you wanted. It just wouldn't be a very nice description.

>>8962788
Took me 3 days to understand it, so you're doing great by my books

>>8962905
Its not as a ring. Idk about as a group.

>>8962944
The fact you understood it eventually means you have surpassed 50% of math undergrads. So 3 days itself is not bad. ;)

Let [math]\Sigma[/math] be a genus [math]g[/math] surface and let [math]\mathcal{M}_g[/math] be its mapping class group. We assign [math]2g[/math] level-[math]k[/math] integrable highest weights [math]\mu_1,\mu_1^*,\dots,\mu_g,\mu_g^* \in P^+(k)[/math], onto [math]2g[/math] points on the Riemann sphere and let [math] V_{\mu,\mu^*} = V_{\mu_1,\mu_1^*,\dots, \mu_g,\mu_g^*}[/math] be the space of conformal blocks of the CFT that satisfy the KZ monodromy. A TQFT functor can be defined that maps the surface [math]\Sigma[/math] to the vector space [eqn]V_\Sigma = \bigoplus_{(\mu),(\mu^*)} V_{\mu,\mu^*}.[/eqn] This shows that a TQFT can be constructed from a CFT.
Now let [math]L_1,L_2[/math] be links whose regular neighborhoods are copies [math]H_1,H_2[/math] of [math]H[/math], where [math]\partial H = \Sigma[/math], and denote by [math]M[/math] the 3-manifold obtained by gluing [math]h:\partial H_1 \rightarrow \partial H_2[/math]. Let [math]L(h)[/math] be the link that gives [math]M[/math] upon Dehn surgering [math]S^3[/math] and does not intersect [math]L_1, L_2[/math]. Take [math]T(h) = L \cup L_1 \cup L_2[/math] and let [eqn]\rho(h)_{\mu\nu} = \sqrt{S_{0\mu}}\sqrt{S_{0\nu}}C^{\sigma(L(h))}\sum_{\lambda:\{1,\dots,m\}\rightarrow P^+(k)} S_{0\lambda}J(T(h);\lambda)_{\mu\nu}[/eqn] via Witten's tangle operator [math]J(T(h);\lambda)_{\mu\nu}: V_{\mu,\mu^*} \rightarrow V_{\nu.\nu^*}[/math], where [math]S_{0\mu} = \prod_{i}S_{0\mu_i}[/math]. The map [math]\rho = \bigoplus_{\mu\nu}\rho_{\mu\nu}: \mathcal{M}_g \rightarrow GL(V_\Sigma)[/math] is a projectively linear representation that satisfies [math]\rho(fg) = \xi(f,g)\rho(f)\rho(g)[/math], where [math]\xi(f,g) = C^{\sigma(L(f)\cup L(g))-\sigma(L(f))-\sigma(L(g))} \in \mathbb{C}^*[/math]. This shows that the TQFT is unitary and not anomaly-free.
This construction gives me an idea of what sort of geometric data can be recovered from a TQFT, and how I can incorporate it into the space structure of a TQFT to describe AdS/CFT.

>>8962911
>Even if you have to use the Schroeder-Bernstein theorem, the proof of it is constructive
no it's not

What should I be studying if I want to prove things involving diophantine equations?

>>8963245
really depends on the diophantine equation, you might get something easy enough to work with using techniques from elementary number theory (i.e. pell's equation), or you might be looking at fermat's equation and need things from algebraic geometry, representation theory, modular forms, etc..

>>8963023
All this work and no replies, you deserve a reply, hear it is!

Given that we are able to obtain a TQFT from a CFT by constructing a modular functor from the conformal blocks, perhaps we can reverse engineer the construction to obtain a CFT from a TQFT.
My idea is to equip the space structure of an unitary decorated TQFT with a set of points [math]p_1,\dots,p_{2g} \in \mathbb{C}\cup \{\infty\}[/math] where [math]g[/math] is the genus of the surfaces [math]\Sigma \in \mathscr{A}[/math], such that the TQFT functor maps these set of points to the "KZ structure" on the conformal block [math]V_{\Sigma}[/math], i.e. it would ensure that the covariant tensors [math]\Phi \in \operatorname{Hom}(V_{\mu_1}\otimes V_{\mu_1^*} \otimes \dots \otimes V_{\mu_g}\otimes V_{\mu_g^*},\mathbb{C})[/math] satisfy the KZ equation [eqn]d\Phi = \omega \Phi[/eqn], where the KZ form
is given by [math]\omega = \frac{1}{k-2}\sum_{i < j}\Omega^{(i,j)}d \ln(z_i - z_j)[/math], and fibres over to a linear bundle [math]\varEpsilon(p_1,\dots,p_{2g})[/math] with a flat connection [math]\nabla = d - \omega[/math]. The TQFT functor maps [math](\Sigma,\{p_i\})[/math] to the space of conformal blocks [math]V_{\nu,\mu^*}[/math] in the sense of CFT, and then I will make sure that everything else also works as expected and that the operator invariant for this TQFT correspond to Witten's invariant. This will give me a pretty promising framework to base the AdS/CFT correspondence on.
>>8963259
Thanks anon.

>>8963323
>typos
It should be [math]\mathca{E}(p_1,\dots,p_{2g})[/math] and [math]V_{\mu,\mu^*}[/math].

>>8963323
JUST
U
S
T
It should be [math]\mathcal{E}(p_1,\dots,p_{2g})[/math] and [math]V_{\mu,\mu^*}[/math].

>>8962450
Someone needs to shoop that picture with some more appropriate /sci/ reading.

>>8962568
so you are saying if there is a bijection QxQ->Q, the cardinality of QxQ is the cardinality of Q?

I basically have to find the smallest natural number n for [math] a^n\equiv 1 (mod 100) [/math].
I get a solution (n=40) with Euler's theorem, but how do I proof that 40 is the smallest solution or if it is not the smallest solution how do I get to the smallest one?

>>8963391
>if there is a bijection QxQ->Q, the cardinality of QxQ is the cardinality of Q?
of course, there's a bijection between two sets if and only if the two sets have the same cardinality

>>8963394
you need more details here, specifically conditions on this 'a'

for example if a=0 then a^40 is not 1 mod 100

>>8963394
Well, you could just use a cas, e.g. maple, to brute-force check for [math]1\leq n \leq 39[/math], but this i probably not what you want. Also, if this is not only for some specific [math]a[/math], need what >>8963399 already said.

>>8963399
>>8963406
Oops, forgot to add that a is any integer with gcd(a,100)=1 .

>>8963423
you have phi(100)=40 but there's no primitive root mod 100 so (Z/100Z)^x is a non-cyclic group of order 40

so by the fundamental theorem of finitely generated abelian groups (Z/100Z)^x is either Z/2Z x Z/2Z x Z/2Z x Z/5Z or Z/4Z x Z/2Z x Z/5Z, which tells you the smallest n is either 10 or 20

>>8963477
Ok, seems like the smallest n is 20. But is there a way to get that answer with just Euclid's theorem and some other really basic number theory stuff? Like "Euclid gives 40, but because of xyz we can cut it down to 20"

No primitive roots or groups, that's already too advanced. This is for students 2 months into number theory.

>>8963492
Bump. The problem is:

Find the smallest number [math] n \in \mathbb{N} [/math] that satisfies [math] a^n \equiv 1(mod100) [/math] for all [math] a \in \mathbb{Z} [/math] with [math] gcd(a,100)=1 [/math] .

>>8963492
primitive roots are pretty basic, what other theorems has your class covered?

>>8963593
Euclid, Euler, [math] \phi (n), \tau (n), \sigma (n) [/math] , multiplicative functions, Wilson, some basic stuff about primes, modulo (including the Chinese Remainder Theorem). Things like that.

anyone able to give a broad rundown on the current state of motives?

i get that there's all these different pure motives, mixed motives, chow motives, tate motives, artin-tate motives, and that some are basically supposed to be the ideal building blocks to work with in algebraic geometry, but the 'right' category of motives hasn't been found yet? i've seen tate motives used in vast generalizations of birch swinnerton-dyer conjecture but I've never really seen some kind of introductory book on motives, just scattered research papers

>>8963627
>I've never really seen some kind of introductory book on motives, just scattered research papers
also on this point is it fair to compare motives to something like L-functions, where the definition depends on the setting but all L-functions generally have the same flavor? and so we wouldn't expect a book on 'general' motives like we wouldn't expect a book on 'general' L-functions

>>8963006
Thanks friendo

@8963627
@8963629
>>>/a/

>>8962385
I have interests in the theory of dynamical systems, the theory of functionals, real analysis, complex analysis, tensor analysis, and numerical analysis. In numerical analysis, I have an interest in developing algorithms whose error terms can be correlated with decoherence and/or violation of conservation of information in quantum theory. I have also been working on non-coordinate bases for general relativity and I think number theory is relevant to my interests in this regard.

The specific "new" thing I have been trying to break into is the analysis of hyperreal numbers. Classical field theory is extended into quantum field theory by extending the real numbers into the complex numbers and I want to study how to extend that to "hypercomplex" field theory by applying the concepts of hyperreal analysis to the real and imaginary number lines in the domain of QFT field variables. The goal in this regard is to explore the solutions to the Hamiltonian action principle that are maxima of the action. Usually the minimum action is selected because the maximum action is almost always infinity but I think I am developing a good workaround based on hyperreal numbers. I think this could equally well be a problem in dynamics or analysis.

I have a lot of well-developed applications in mathematical physics, but recently I came up with a purely mathematical application of the principles I have been struggling to make rigorous (and failing to do so because I am not a proper mathematician). In the link below I hope you find a thoughtful and well-reasoned argument against the Riemann hypothesis (that hopefully also has an application to the axial current anomaly in QCD). This is not what I consider one of my best results but it is one that can be understood without having to go into the nested references of my other papers.

>On The Riemann Zeta Function
>http://vixra.org/abs/1703.0073

Sophomore here. I want to focus on something related to topology next year, but I don't know exactly what. I thought I'd go for K-theory, since I'm arleady kinda good with basic algebraic topology, although homological algebra is a viscious bitch when it is detached from topology.

Anyways, if you were a young student aiming to get to a good grade school eventually and knows some very basic topology, what would you go for?

>>8963714
Go back to Tumblr

>>8963738
>>/sci/image/g3R37MfrTJnr_nL6BVuNBQ
>>/sci/image/QpPyH3NmVNNiB8q6YrbFhQ
who were you quoting in all of these posts?

>>8963747
the guy you're responding to isn't me

>>8963748
oh, sorry
>>/sci/image/g3R37MfrTJnr_nL6BVuNBQ
>>/sci/image/QpPyH3NmVNNiB8q6YrbFhQ
>>/sci/image/Gz3urX5eLH5x02UE2WfVkg
who were you quoting in all of these posts?

>>8963751
>who were you quoting in all of these posts?
what do you mean? you can see the post number i quoted in each, i assume they're mostly anonymous

>>8963752
wayq?

>>8963754
you lost me m8

>>8963755
>>>/global/rules/13

>>8963758
reaction images aren't avatars m8

>>8963759
Unfortunately you got baited into admitting you're an avatarfag, so see yah I guess lol

>>8963760
>Unfortunately you got baited into admitting you're an avatarfag
which post was that in?

>>8963759
>>8963758

13) Do not use avatars or attach signatures to your posts.

t. rulefag

When will we have AI strong enough to be able to search the math literature to see if combinations of theorems can prove new ones?

I'm desperately trying to understand why the divisor [math](\pi^*(A) - dE)[/math] defines a morphisms that becomes [math]/phi_{\bar{k}}[/math] when you base extend to [math]\bar{k}[/math]. I've been feeling like a brainlet since I started working on that proof.

>>8963832
That [math]/phi_{\bar{k}}[/math] should be a [math]\psi_{\bar{k}}[/math]

>>8963737
Homological Algebra is really abstract subject, but once you get the hang of it it is actually pretty easy.

>>8963737
>grade school
Symplectic geometry. The geometric quantization people desperately need new talents.

>>8963737
why not master topology

>>8963737
From the sounds of it, you don't know a whole lot.

Personally, I would go algebraic geometry if I were able to start over from highschool.

>>8962385
Math student here. How do I git gud at triple integrals?

And I don't mean how to compute antiderivatives, change variables, limits of integration, etc. I know all that.

I mean about when you FEEL the integral. How do I FEEL the triple integral? I remember back when doing normal integrals I could FEEL mistakes, and I could also FEEL when my solution was right. What I did was that after integrating I would then mentally calculate an estimate of the area under the curve and see how close my result is to my estimate.

But how can I estimate what I can't FEEL? If I am doing triple integrals for volume then I can't really estimate 3d volumes as well as I could estimate areas under curves mentally. And if the integral is literally 4D then my brain can not even try to feel it.

So how do geniuses do it? I need to feel triple integrals. I have never been able to do math that I cannot feel and I worry that I may get something less than an A for the first time in my life because I can't really feel the integrals.

>>8964506
Rewrite your post in a less retarded way if you want an answer from me.

>>8964506
I usually feel integrals by printing out a 3d model of the equation and turning it around in my hands for a few hours.

If that doesn't work, I sometimes laser etch the equation onto my butt plug. It helps to feel it from the inside

>>8964506
>muh feels
All of my what.

>>8964526
How do I feel triple integrals?

>>8964566
If you don't can't feel mathematics then you are not going to make it my brother. Better drop out and change majors before it hurts.

>>8962450
What is she doing....?

>>8964561
>I usually feel integrals by printing out a 3d model of the equation and turning it around in my hands for a few hours.

I wish I could do this but first I can't really bring a 3D printer during a test (and while I love calculus, my current primary concern is being able to pass this final round with an A) and second I have no 3D printer.

Therefore, as has often been the case, I have to feel it. Mentally. I need to in some way feel connected to integrals like I feel connected to ideals, groups, rings, vector spaces, single integrals, double integrals, topologies, etc.

>>8963799
Category theory already does that.
>find duality/equivalence between categories
>formalize theorems in them in terms of categorical language
>see how it behaves under the duality/equivalence
>???
>profit
You can probably do this with Coq or other Turing-complete language that has a closed compact monoidal category of types.

I have two conundrums. The first one is that I can try and have another go at an exam I did badly in and maybe get an honorable grade (or whatever it's called, it's the thing they give you when you have the best grade), but it also substitutes my original result, so if I fuck up then I'm fucked for good. If I don't do anything I'll have an 8. What should I do?

The second one is that I'm interested to do my Master's in Cambridge, but I'm starting to realise that there's no fucking way I'm getting in (I know of two people going there next year, and their average grade is ~9.7). I went and asked my advisor about it and it looked like he simply didn't want to tell me that I'm beyond fucked. So I want to know what I'll be missing and how much I should care (stupid, I know).

Also I'm a worthless piece of trash.

>>8964788
>it also substitutes my original result
Are you sure?
>I'm interested to do my Master's in Cambridge
What for? Do you want to do maths or do you want to acquire social prestige?

>>8964788
>the thing they give you when you have the best grade
The word is "distinction".

Do more research and get a paper published, and try to sound passionate during interviews. If you don't have the grades at least have the research skills and drive to back it up.
Also I hope your grades increased throughout undergrad, or you're fucked.

>>8964973
>What for? Do you want to do maths or do you want to acquire social prestige?
I want to do good maths, to feel I deserve the respect people have for me and for more people to respect me.
>>8965020
They did (probably not by enough, though), but I'm already convinced that I'm beyond fucked, and no way I'm getting anything published and beating the competition for the few places they have. I just want to know what I'll be missing out, and if there's any way to at least be as good a mathematician as someone getting their master's there.

>>8965034
Do masters elsewhere mate lmfao

>>8965034
>what I'll be missing out
Nothing.
>if there's any way to at least be as good a mathematician as someone getting their master's there.
Where you're getting your degree is irrelevant. If you have the knack for math you got it, if you don't have it, you don't have it. Institutions are a filter, nothing more. They don't impart anything on you.
>to feel I deserve the respect people have for me and for more people to respect me.
So you just want prestige. Try to switch majors. I recommend marketing.

>>8965096
Amen.

>>8965096
>Where you're getting your degree is irrelevant

>>8965103
EPIC reddit meme LOL!!!!! You are making a very FUNNY comment chain!!!!! GOLD!!!!

>>8965108
>Institutions are a filter, nothing more.
>They don't impart anything on you.
is this how you cope with going to a no name school? GOLD!!!

>>8965109
That wasn't me, frogposting retard.
>GOLD!!!
hahahahaha LOL!!! Epic meme breh!!!

>>8965109
>>8965103
Is this how _you_ cope? It's readily apparent you are trying to compensate for something.

>>8965103
>>8965109
I can't bear to see this retardation.

>>8965113
>It's readily apparent you are trying to compensate for something.
oh please elaborate, I'd love to hear what you think I could be compensating for by not deluding myself into living in a bubble where reputation and prestige don't affect reality

you're not serious are you?

>>8965103
>>8965109
Fuck off idiot.

>>8965103
>/sci/ poster
>completely unfamiliar with the research
Pick both. As far as your ability to do maths is concerned, which is what I was talking about, yes, it's irrelevant. The best universities are those which select for the best students.

>>8965117
woww!!!!! amazing!!! upvoted!!!!!!!
BBBBBBBBBRRRRRRRRRRRAAAAAAAAAAAPPPPPPPPPPPPPPPPP

>>8965117
HAHAHAHHAHAHA THIS THREAD MAN LMAO HEHEHEHEHHEHEHEHEHEHEHHEHEHEH

>>8965103
>>8965109
>>8965117
haha yeah dude we're the cool kids now
!!!

>>8965103
>>8965109
>>8965117
i'm just gonna KILL EM
BBBBBBRRRRRRRRPPPPPPFFFFFFFFFFFFFFFFFFFFFTTTTTTTTTTT
*snifffff*

>>8965122
>completely unfamiliar with the research
"the research", wow you convinced me!

>As far as your ability to do maths is concerned, which is what I was talking about, yes, it's irrelevant.
oh if all we care about is math ability why even go to a university, degrees are just a filter too, nothing more!

please keep it coming this is hilarious

let's go take a look at a good university and see where the people who work there got their degrees

https://www.math.princeton.edu/directory/faculty

>Michael Aizenman
>Yeshiva University

>Sun-Yung Alice Chang
>Berkeley

>Otis Chodosh
>Stanford

>Maria Chudnovsky
>Princeton

>Peter Constantin
>The Hebrew University of Jerusalem

>Mihalis Dafermos
>Princeton

the list goes on and on... what a strange absence of people from no name schools!

>>8965145
>thinking this is somehow inconsistent with the fact that a degree is just a filter
Hello retard. Which community college did you go to?

>>8965145
Fucken lel !!!
Epic IMAGE!!!! GOLD!!!!!!!!!!!!!!!!!!!!!!!!!!

>>8965151
>Which community college did you go to?
none! remember, institutions and degrees are a filter!

keep it coming! best laughs I've had all day

>>8965164
haha yeah dude
!!!! fucken LMAO!!!!!! rofl!!!!
>best laughs I've had all day
HAHAH!!! SAMEE!!! GOLD!!!

>>8965164
>still not getting it
What is an idiot with a room temperature IQ doing in this thread?

>>8965173
>>still not getting it
please, explain it friend! hit me up with another of your high quality posts! the damage control and coping mechanisms are fascinating to observe!

>>8965178
HAHAHAH!!!!! MEMEEE!! PEPE!!!! MEMES!!!
BBBBBBRRRRRRRAAAAAAAPPPPPPPFFFFFFFFLLLLLLLLLPPPPPPPPPFFFFFF

>>8965178
>explain it to me
Not possible. You're too retarded to understand how sorting works. Don't be alarmed though, your woes have a simple solution: suicide.

>>8965189
>Not possible. You're too retarded to understand how sorting works. Don't be alarmed though, your woes have a simple solution: suicide.
there it is! more backpedaling, just on time!

thanks my man, it's been fun!

>>8965190
XDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
Fucken EPIC MY dude!!! This is a VERY FUNNY IMAGE!!!!

>>8965103
>>8965109
>>8965117
>>8965145
>>8965164
>>8965178
>>8965190
Fuck off to some other board, subhuman trash.

>>8962385
/sci/ r8 my textbook

>>8965145
>hurr durr
https://www.ets.org/s/pdf/23497_Angoff%20Report-web.pdf

>>8965215
>using data about high school education and test scores
HAHAHA, I forgot we were talking about high school 'degrees'! I slipped up and thought we were talking about graduate math programs!

>>8965096
Math makes me genuinely happy like nothing else, anon. And I never talked about prestige, I talked about respect. If I'd like to go to Cambridge it's because I feel I'll learn more math there than anywhere else, and I'd never use where I've studied as a ploy for cheap respect. It's a dirty tactic.

>what are you studying?

The exact answer is Quantum Computing, but right now I'm starting to get really into quantum mechanics, studying the deep basis.

>any cool problems?
The qubit. The quantization of a bit, by Schumacher compress.

>any cool theorems or remakrs?

I really like the many worlds comprehension, it's a bit too fantastic, but still pretty awesome.

>reference suggestions?

Would recommend the youtube channel "PBS Space Time" for newbies. They have a playlist with 9 videos on quantum mechanics and comprehensions of the universe.

>>8965233
>I never talked about prestige, I talked about respect.
Same difference.
>I'd like to go to Cambridge it's because I feel I'll learn more math there than anywhere else
Your impression is mistaken. How much math you learn depends almost entirely on you. Assuming where you studied made much of a difference (and again, it doesn't), I'd aim for ENS Paris instead. It "produced" 11 Fields medalists (which is even more impressive on a per capita basis).

>>8965233
I'm not that guy but mathematicians don't get any prestige or respect. Mostly what they get are people who are confused about what mathematicians do and ask them mental math questions.

The only reason that shit is a meme is because of movies that make it look like mathematicians are swimming in respect and reverence. Even the university math buildings they work at are often underfunded and ghetto as fuck.

>>8965272
When I say I want respect, I mean it from other mathematicians. I want to know that I'm not dead weight to the community I want to be part of. I already get plenty of social recognition from my peers (which I feel is undeserved), I'm talking about it from a proffessional perspective.

>>8965284
In general, no mathematician will look down on you because you did your master's at some university they have never heard of.

>>8965295
This. However at the same time most mathematicians won't hold you in high regard unless you're doing research in their area and they're familiar with your work. That means that for the majority of mathematicians out there you will be more or less completely irrelevant.

After some thought, the points [math]\{p_i\}[/math] could just be attached to the the arcs [math]L = \bigcup_i L_i[/math] inside the decorated 3-manifold [math]M\in \mathscr{B}[/math] that end on [math]\partial M[/math] after chopping [math]M[/math] up with a cut system of discs [math]C_i[/math] with [math]C_i \cap L_j \neq \emptyset \iff i \neq j[/math]. This means that I could go straight to enriching the space structure with CFTs on [math]\{p_i\}[/math].
I think the best and most straightforward way to do this is to equip each [math]\Sigma \in \mathscr{A}[/math] with an Laurent series affine Lie algebra-valued KZ 1-form [math]\omega \in \hat{\mathfrak{g}}_{\mathbb{C}}(t_1,\dots,t_{2g}) \otimes \Lambda^1(\Sigma)[/math] such that the embedding [math]\operatorname{Hom}(V_{\mu_1}\otimes V_{\mu_1^*}\otimes,\dots,\otimes V_{\mu_g}\otimes V_{\mu_g^*},\mathbb{C})
\hookrightarrow V_{\mu_1 \mu_1^*\dots \mu_g\mu_g^*}[/math], whence [math]\Phi \in V_{\mu_1 \mu_1^*\dots \mu_g\mu_g^*} \iff d\Phi = \omega \Phi[/math], exists, and that [math]\omega[/math] induces a flat connection [math]\nabla = d - \omega[/math] on a fibration of the conformal blocks [math]\mathcal{E}(p_1,\dots,p_{2g}) \rightarrow V_{\mu_1 \mu_1^*\dots \mu_g\mu_g^*}[/math]. This will ensure that [math]\Phi[/math] is a conformal block invariant under the diagonal action of the affine Lie algebra [math]\hat{\mathfrak{g}}_{\mathbb{C}}(t_1,\dots,t_{2g})[/math], which will in turn generate the conformal algebra. The TQFT functor will then map cobordisms to homomorphisms of the space of conformal blocks.
This characterization of the CFT [math]\mathscr{T}(M,\omega)[/math] by the conformal algebra is enough to guarantee naturality and uniqueness, and the only major thing to do afterwards is to make sure that Witten's invariant can be obtained from the operator invariant of this TQFT.

>>8965351
nigga what kind of language is this

>>8965351
Fuck that should be [math]C_i \cap L_j = \emptyset \iff i \neq j[/math], and also I should specify that [math]C_i \cap L_i = \{p_i\}[/math] (the singleton).
>>8965362
Memes.

>make sure that Witten's invariant can be obtained from the operator invariant of this TQFT
I will save you some time: it can't.

>>8965404
Nope, I think that's actually the part that's doable, since by Heegaar splitting [math]M = H_g \cup_h H_g[/math] it can be shown (see Kohno, Turaev) that the dimensionality of Witten's invariant can be calculated as [math]\operatorname{Dim}(Z_k(M)) = S_{00}^{-g+1}\sum_{\lambda: \{1,\dots,m\}\rightarrow P^+(k)} \operatorname{tr}_\lambda \rho(h)[/math], where the trace is taken over the space of conformal blocks with the highest weights [math]\lambda[/math], purely from the CFT perspective while that of an operator invariant [math]\tau[/math] of a decorated TQFT can be shown to be [math]\operatorname{Dim}(\Psi_t) = (\mathscr{D}^2)^{g-1}\sum_{j\in I} \operatorname{dim}(j)^{2-2g}[/math], where [math]I[/math] is the set of colorings by [math]\{1,\dots,m\}[/math] of the ribbon graph of type [math]t[/math] in the decorated 3-manifold [math]M[/math], purely from the TQFT perspective. I believe I would be able to massage my TQFT so that the the colorings in the latter expression correspond to labelings of 3-valent graphs that satisfy quantum Clebsch-Gordan conditions, which will automatically guarantee that the sums in each expression coincide. And after this dimensionality check there isn't much else that the operator invariant of my TQFT could be other than something that is at least projectively isomorphic to Witten's invariant.
Good question anon.

This might not be the appropriate place to ask this, but I'm not really sure which grad schools I should be aiming at / applying for.

I want to study (pure) math - I'm interested in number theory / algebraic geometry, but I'm open to other things.

What range of programs should I be applying for if this is my background?

As for courses completed in freshman-junior year,
Undergrad: Abstract / linear algebra, 3 semesters of real analysis (on the level of Rudin), numerical analysis, 2 semesters of statistics (theory)

Graduate: Algebraic number theory (2 semesters), algebraic geometry, abstract algebra 2, measure theory, topology, complex analysis, and a special topics course on geometric analysis.

I'm also doing a reading course with a professor on commutative algebra, and doing a (small) research project with him as well, probably nothing that would lead to a publication.
I go to a school ranked ~25-30 for grad programs.

I also have (almost) a 4.0 gpa.

Do I have a shot at top-10 programs?

>>8965449
what quality would you expect your letters of recommendation to be?

>>8965457
Good but perhaps not excellent.

I stand out in class as the youngest and I speak up a decent amount, and I think I make a good impression during office hours.

I haven't had a ton of contact with my professors otherwise though

>>8962385
how do i become the next mochizuki ?

>>8965449
I think top 10 is probably reasonable, though it's going to depend on if the recs and gre scores are good. You should talk to professors from your department for guidance, they'll have a better idea about which schools are reasonable than anyone on /sci/.

>>8965449
Why does he get adviced on how to go to a top 10 program but when I bicker on how I'll never be able to do such a thing I'm told that it doesn't really matter and that I should just be myself and work real hard? Why the double standard?

>>8965719
Because he doesn't say stupid shit like "I do math for respect".

>>8965719
There is no double standard.

>>8965778
Anon, I don't do math for respect, I'd still do math regardless. It's just that others' respect is the only way I have to gauge myself and feel valued, because I have an extremely unhealthy view of myself that I can't seem to cure no matter how much I try. I have no self-esteem and I depend on others for it.

But thank you for being tough on me. I feel like I'm completely missing the point of it all and you're being helpful, unlike people sometimes are in my real life (no sarcasm intended).

>>8965787
>There is no double standard.
Explain it to me please. I don't understand and I really want to.

>>8965794
>Explain
It doesn't matter where that guy does maths either. You're getting different answers because you're asking different questions.

Any book that explains fractions better and more in depth?
Khan just doesn't work for me somehow.

>>8965449
A solid of pure math classes with many grad classes is always a good sign, plus gpa wise you couldn't do better (literally, unless you go to a school with a +/- grading system). Grad schools like this as it shows consistency in education and work ethic. It should be noted however that this isn't all grad schools are looking for, sure, it'll get you into most programs, but the best ones look for more, namely they want some form of research to show you've got the chops to finish the program (not necessarily published, a quality senior honors thesis is also good, though published research in good journals will take you VERY far towards getting accepted) this also serves a second purpose, working with a professor so that they can evaluate your skill set and be a judge of character, which is part of what the letters of rec are about, how experts evaluate you. Good research and great letters of rec can put you over the top at a lot of great schools, great research and fantastic letters of rec will get you into the top schools, in many times cases even over candidates who have higher gpas from more reputable schools, an example of this I know of was an undergrad who worked in my group before me, our math program is ranked somewhere between 50-75, nothing super impressive, though not terrible, he also didn't have the highest gpa at a 3.7 but still he was able to get into Harvard and an nsf grad grant, what set him over the top was his name on 4-6 papers sent to pretty good journals and glowing hot letters of rec. To max your chances focus more on research in your last year, though don't let your gpa slip, also crush the gre, a good score on it never hurts. Finally don;t get caught up in a school's prestige, I know I just mentioned Harvard but that was because I wanted to point out that it is possible to get through even the most draconian of selection processes.

>>8965449
>>8965934
Another good part of research is the ability to familiarize yourself with the field and find out who does what (your prof should also help with this) once you find which specific things you want to do (i.e. field and work inside the field) you should apply to grad schools where those experts are, sometimes they are at top 10 schools, many times not, remember, you're applying to grad school to work under a professor and get a phd, the prof matters, not the school, for example, john klauder is a world class mathematical physicist, but he's at the university of florida right now, vanderbilt has a decent grad program, but if you want to do noncommutative geometry there is no better place, conversely if you want to go to Harvard and do combinatorics or functional analysis you're shit out of luck, ucla would be a far better fit, so focus on who you want to work with, not where. Your prof should know who works in the field and who should be a good fit for you (hell he might know many of them personally) so when he writes those letters of rec and his friends at other schools who are experts read them it carries a hell of a lot more weight than if they never knew who he was. Another thing they like is outside activities like going to conferences, poster talks, seminars, presentations, and in many cases club activities like being the president of you pi sigma epsilon club or volunteering/mentoring these serve to help you interact with the community and show that you'll be able to deal with all the non-math related stuff that goes into being a mathematician (bureaucratic bs, conference environment, giving a decent talk, teaching, dealing with other mathematicians, yada yada).

>>8965719
Cause it appears that he's already working hard to get into the best programs he can

>>8965937
>Cause it appears that he's already working hard to get into the best programs he can
That's fair enough. I only started working hard this third year because I fell real hard for the "smart but lazy" and "grades don't matter in uni" memes, and now I'm paying for it.

>>8965937
>Cause it appears that he's already working hard to get into the best programs he can
Or in translation: because he seems to have what it takes.

>>8965968
I wanto to know what's your opinion on the matter, anon.

>>8965971
Which one are you?

>>8965983
The one that hasn't worked hard.

>>8965985
Can you solve that puzzle without using any form of aid like pen&paper?

>>8965987
No.

>>8965993
Why give up so fast? It took me almost 15 minutes to figure it out. (But if you can't solve it, you're not "smart but lazy". You're not that smart and lazy. Which means grad school at Cambridge is beyond your reach.)

>>8965999
I'm still trying, I just already know the outcome. Also, when I said I fell for the meme I meant to imply that I didn't realise I'm not smart at all. Also, is there any way to prove that the solution is the only valid solution possible?

>>8966002
>I'm not smart at all
Hard to reach senior year studying math while being dumb. So you know, about half of mathematics and physics PhDs can't solve that puzzle. The proportion is even higher for people with PhDs in other subjects.
>is there any way to prove that the solution is the only valid solution possible?
Yes. The pattern is deterministic.

>>8966035
>Hard to reach senior year studying math while being dumb.
whew you must have gone to a school of brainiacs

>>8965999
>But if you can't solve it, you're not "smart but lazy". You're not that smart and lazy
>>8966035
>Hard to reach senior year studying math while being dumb. So you know, about half of mathematics and physics PhDs can't solve that puzzle. The proportion is even higher for people with PhDs in other subjects.

I don't understand.

>>8966040
Not that smart =/= not smart. ESL?

>>8966043
>ESL?
What's this?

>>8966039
Define "school for brainiacs". I was rejected by Cambridge.

>>8966047
>Define "school for brainiacs".
my school had plenty of people doing their math degrees who i would never label as smart, either people who cheated their way through (googling all their homework), people who took all the easiest classes, or people who just didn't seem to put the effort into harder classes

>I was rejected by Cambridge
for part III? i got accepted but w/o funding so i didn't go

>>8966056
>for part III?
Yes.

>>8965983
what's the answer

>>8966064
On each row of blocks, move every symbol (circle, cross, triangle) to the right with carriage to the next row of symbols. Then change circles into triangles, triangles into crosses, and crosses into circles.

>>8966078
So it's:
^ o o
^ ^ o
x x x

>>8966078
What made you realise that was the answer? When I try these kinds of puzzles I always get stuck with the endless possibilities and I end up overcomplicating everything, but it's also true that I never know beforehand how difficult or contrived it's supposed to be in the first place, so I simply get lost.

Did you just come up with reasonable things and tried them out, or did you do something more subtle and involved?

>>8964788
>>8966002
If you want to know what part III is like many of the course notes and problems are freely available online, just do it yourself, no reason not to provided that your reason for wanting to go to Cambridge is the you heavily care about the educational content and not the name.

>>8962452
Do cashews and wallnuts count?

>>8966096
It's what I'll try to do, starting this summer, but I don't think I'll do as well.

>>8966101
These things take time, part III isn't considered to be one of the most intensive math programs on the planet for nothing, the point is actually learning the material, and that can always be accomplished with time, mental fortitude, and a fuck ton of effort.

>>8966103
Thanks for the encouragement, anon.

>>8966091
I really don't know how to explain it. it kinda just popped up in my head. I visualised the symbols move and change. The fact that each block is divided by a grid seemed suggestive to me, so I started to focus on the symbols instead of the block as a whole. The rest is just verification. As an extra check, the pattern holds for columns too (move symbols top to bottom with carriage on the column to the right), and it gives the same answer.

>>8965983
I recognize that test.

http://iqtest.dk/main.swf

First time I only got 137 IQ or something because I did not understand 3 of the puzzles. Now I understand them all and can explain to you the solutions if you want.

>>8962788
It's quite intuitive, once you get it, but the formal definition is always hard to understand at first.

>>8966124
No need. I get 145+ too. (Having the generating function on each problem explained to you just spoils the results by the way.)

>>8966078
i'm never coming on this site again

>>8966144
why?

>>8963323
>I'll never understand any of this

>it's an anon suffers from impostor syndrome episode

>>8966188
Who are you talking about?

>>8965934
>>8965937
>>8965591
Cool, thanks for the advice guys.

I'll still have all of senior year to take courses, and I'll be working on an honors thesis as well.

What's a decent GRE score? I've heard 80%+.

I'll definitely take the one anon's advice and talk to people in the department who know me for more specific details.

>>8966186
Don't worry. It means almost nothing.

>>8966294
Depends on the school, though really as long as your other areas are solid it won't really make or break you, still strive to get 80%+ though, it's just another box to check.

Analyst wannabe here. I have to prove that
[eqn]\int_{2}^{x} \frac{\vartheta(t)}{t log^2 t} dt = O \left( \frac{x}{log^2 x} \right) [/eqn] where [math] \vartheta(x) [/math] is Chebyshev's [math] \vartheta [/math]-function.

I just have my books and no one to grade me so I will share my solution.

Proof:
I start by computing [math] \frac{d}{dx} \frac{x}{log^2(x)} = \frac{log(x) - 2}{log^3(x)} = O \left( \frac{1}{log x} \right ) [/math]
And therefore:
[math]\frac{x}{log^2 x} = O\left(\int_{0}^{x} \frac{dt}{log t} \right ) [/math]
And noting that [math] \vartheta(x) \leq xlogx [/math] and from this last thing I get that:

[math] \int_{2}^{x} \frac{\vartheta(t)}{t log^2 t} dt = O \left( \int_{2}^{x} \frac{dt}{log t} \right ) = O \left( \int_{0}^{x} \frac{dt}{log t} \right ) =
O \left( \frac{x}{log^2 x} \right)[/math]

Is this a valid proof?

>>8966328
seriously?

>>8966424
it's kind of like that jonathan tooker fellow from the last thread...

>>8966328
Please direct your confusion and frustration to me instead of responding passive aggressively to innocent bystanders.
>>8966424
To him it doesn't. Most things don't either I imagine.

>>8966615
His idea is may be a stretch, but the actual stuff he is posting is sound. That jonathan tooker guy just made stuff up that has nothing to do with actual physics.

>>8966616
Some questions:
(did you perhaps mean to write Dehn surgery instead of surgering?)
what is (Witten's) tangle operator?
decorated manifolds as per https://arxiv.org/abs/1511.03851 ?
>(see Kohno, Turaev)
which papers god damn you? not everyone is familiar with the literature you're reading.
>>8966633
Tell me why I should trust you.

>>8966658
>(did you perhaps mean to write Dehn surgery instead of surgering?)
I'm using the term as a verb. Surgering is the (relatively) commonly accepted verbal form of surgery, at least in the context of knot theory. It's used in Turaev anyway.
>what is (Witten's) tangle operator?
It's an operator invariant of links and 3-manifolds that can be constructed from a CFT. It's an example of this https://en.wikipedia.org/wiki/Quantum_invariant..
You can also see the previous thread where I defined it roughly.
>decorated manifolds as per https://arxiv.org/abs/1511.03851 ?
As per the book "Quantum Invariants of Knots and 3-Manifolds" by Turaev. Decorated manifolds are manifolds equipped with ribbon graphs labeled by objects and morphisms of a semisimple category embedded inside a 3-manifold.
>which papers god damn you? not everyone is familiar with the literature you're reading.
They're both books. "Conformal Field Theory and Topology" by Takahashi Kohno and the aforementioned by Turaev.
>>8966633
It might not be such a stretch after all. In Kohno (p.120) he described an alternative definition of Witten's tangle invariant by doing exactly what I did: assigning highest weights [/math]\lambda\in P^+(k)[/math] to the components of links [math]L[/math] in a decorated 3-manifold. This shows that what I've focused on is in essence
a part of the "canonical" correspondence between unitary TQFTs and CFTs.
I've just read this btw, pretty interesting to see my idea show up on paper.

>>8966658
by the way I'm not >>8966615 I am >>8966424
and I've been struggling to read through those posts for the better part of an hour now

>>8966692
ok thanks, I can plough through with some proper references now.

>>8966700
Yeah I figured. People like him aren't the kind that'd be keen to learn.
>>8966709
Good luck anon.

>Be in class
>professor writes down theorem and says he will prove this one for us
>Sit back, relax and enjoy the ride
>In the middle of the proof the professor mentions a fact, not proven before, that will be applied in the final argument but that he won't bother to prove it because it is simple
>I look at the statement and it is not exactly obvious
>autism kicks in
>start to think about why that little lemma is true
>take out my notebook and make some quick manipulations
>make a mental proof of the lemma
>feels good man. Time to go back to paying attention to the board
>"And that is how you prove the Riemann Hypothesis. This will be the class for today, hope you understood the proof. See you next monday".

It should be illegal for professors to just state unproven statements like that in the middle of a proof. It is like if a girl started showing off her tits in the middle of class. I am obviously going to look at her tits, just like I'm obviously going to try to prove the lemma.

Fuck me.

>>8962385
Can someone give me, an enthusiast, a quick rundown on why logs were invented, and a couple examples of calculations done with logs by necessity before electronic calculators were invented?

any info you have on the natural log would also be most graciously received.

>>8967308
>tfw a girl shows you her tits and on her left boob she has an unproven conjecture

Do you look at the tits or prove the conjecture?

>>8967315
https://en.wikipedia.org/wiki/Logarithm#Logarithm_tables.2C_slide_rules.2C_and_historical_applications

>>8967315
>why logs were invented
Because people want to do multiplication quickly, and they found that addition is faster than multiplication so they invented a function that maps the bilinear map [math](a,b) \mapsto ab[/math] to [math](a,b) \mapsto a + b[/math] and then they called it log

>>8967327
is it still useful in modern times? would i be able to do mental arithmetic more quickly if i worked with logs rather than multiplying normally?

>>8967308
>It should be illegal for professors to just state unproven statements like that in the middle of a proof.
why get bogged down in details? if you can prove an important theorem and leave a lemma till later there's nothing wrong with that

>>8967315
>quick rundown

>turn products into sums
>sums are computationally simpler than multiplication
>no need to worry about the problem of computing an actual log if you have already have a table with all the values, or a supercomputer
>trigonometric functions bow down to the logarithms
>in contact with [math] x^{-1} [/math]
>rumored to posess many unproven number theoretic theorems
>control differential equations with an iron fist
>own analysis departments all over the world
>direct descendants of the exponential functions
>will bankroll the first theorems proven in mars
>in the process of terraforming arithmetic
>own basically every exponential base cancelling facility
>first designer functions will be logarithmic functions
>All logarithms said to have 400+ applications in calculus
>ancient indian scriptures tell us of a family of functions that can cancel the base of an exponentiation
>These are the logarithms
>They own analysis R&D labs all over the world
>You likely have logarithms written in your notebook right now
>Every child will be forced to know about them
>Are in regular communication with Shinichi Mochizuki, Terence Tao and Norman Wildberger (but Wildberger does not answer back and pretends they don't exist)
>Discovered applications of the logarithmic integral
>They can be learned in under a week
>Are allowed full access to the real numbers
>Nation states entrust their calculations to them
>The logarithm is 403 years old, from the space-time reference-point of humans
>In reality they are timeless beings that can exist even without humans thinking about them
>They have been able to access the positive real numbers since birth
>the logarithms will guide humanity into a new age of wisdom, peace and love

>>8967335
>why get bogged down in details? if you can prove an important theorem and leave a lemma till later there's nothing wrong with that

That's all good and all but I can't help it.

Think about it like this:
There is a girl showing you her tits right now. Would you take a mental picture of her tits, then look a way, and then jerk off to her tits later? Or would you take the chance and jerk off to her tits immediately?

>>8967342
wew lad

>>8967316
>>>/b/

>>8967354
>he doesn't like tits and mathematics
>>>/lgbt/

Let's be real, we all know it is already time for you to go back.

>>8967347
but as soon as you take your dick out, your chances of having more than a wank increase exponentially

>>8967329
>is it still useful in modern times?
Cute question anon.
The fact that logs make multiplication into addition is the historical motivation for why they're found. There are other important consequences of that that are useful in both mathematics and physics.

>>8967363
actually they increase hyperbolically.

sharp increase for the first few minutes, but if nothing has happened by then, they start to decrease back to baseline, then below baseline for the rest of your relationship with this person

>>8967342
Lmao this is the kind of posts I want more in /math/

hello is true market prolapse soon??

>>8967381
>>>/b/

>>8966692
>>8967368
Gotta ask, what kind of books did you use to learn mathematics and theoretical physics, you seem to at least be doing high level mathematical physics so I'd be nice to know some books to get there.

Also good taste in waifus.

>>8967425
>what kind of books did you use to learn mathematics and theoretical physics
Various. I usually just pick up whatever interests me and start reading. My suggestion is to first familiarize yourself with the underlying mathematics of QFT with either Baez or Strocchi. Bernevig will give you a good introduction to topological orders, and Fujikawa will tell you how these topological orders can manifest in a gauge field theory (like in CS or WZW). Afterwards you can move on to Turaev or Witten for some hard-hitting TQFT. For CFT DiFrancesco is a must read, and Kohno is a very compact and well-written guide to the mathematical foundations of CFT. Incidentally if you're interested in geometric quantization Woodhouse and Guillemin & Sternberg are good books to have.
Also my favorite 2hu is Ran. I just identify with Yukari since she's a smug bitch.

>>8967525
Thanks anon, I'm actually familiar with a decent amount of the mathematics, though from the perspective of mathematicians and not from physicists so its nice to have some books geared towards their physical applications, possibly with a little algebraic geometry as well since it appears that it's used quite frequently. It's also nice to have a list of reading material, it's not hard to find books on tqft/cft, but I've found it to be quite difficult to find pedagogically good books and articles on the subject.

>>8966191
You.

>>8967578
>algebraic geometry
>used frequently in physics
Unless you're doing some weird shit with amplituhedrons you probably won't use algebraic geometry at all. If you meant algebraic topology then there's a very good review article by Mermin that illustrates how cohomology theory can be used to classify defects.

Can someone do an example of solving a multiplication problem using logs, I fail to see how it is not retarded

>>8967525
>I just identify with Yukari since she's a smug bitch.
Avatarfags need to be put down.

>>8967597
I was referring to things like mirror symmetry or moduli spaces and the like, maybe frequently was the wrong word, but from what little I understand some of tools from AG are useful in physics, at least for string theorists. I'm well aware that algebraic topology is used in physics, though I'm not quite sure of it's applications, I'll check out that article.

Any monographs on periodicity?

bumper cars

>>8967621
Algebraic Geometry is used heavily in String Theory. Not so much in other fields of physics though.

>>8968230
>Algebraic Geometry is used heavily in String Theory
So, algebraic geometry is used heavily in mathematics. Got it.

>>8968272
Algebraic Geometry put solid math behind some purely physical objects in String Theory.

Bump
u
m
p

>>8968882

>>8968443
Purely physical objects exist in nature not theory.

>>8962385
This is the 'pair of pants' surface.

>>8969872
Reminder that all closed compact surfaces can be decomposed into gluings of pants.
https://en.wikipedia.org/wiki/Pair_of_pants_(mathematics)#Pants_decompositions

What is the formula for amount of steps it takes to move a tower of Hanoi of n layers on 4 pegs?

I know that 3 pegs is
I know that 3 layers is

[math]2^n - 1[/math]
or
[math]T_0 = 0,[/math]
[math]T_n = 2T_{n-1} + 1[/math]

>>8970408

3 pegs not 3 layers

anyone know how to open FITS files in astropy and plot light curves?

non-mathematician here, what kind of math subjects are at the root of logic and functional relationships between machine components?

How does he calculate the "sin-1" and "cos-1" thing. I am trying to do the same using windows calculator but I can't reach same results

>>8970914
Are you familiar with inverse trig functions?

>>8970920
>>8970920
No

>>8969804

>>8963245
A fun thing you might want to try getting into is p-adic analysis. If you've already taken real analysis and maybe even a little complex analysis you will find that a lot of p-adic analysis is dead simple by comparison and kind of fun once you've ripped your eyeballs out. Specifically aim at the Hasse-Minkowski theorem and local-global prinicple for diophantine equations. Gouvea is a pretty decent intro book.

gonna take real analysis, partial diff eq, and topology next semester. if i do well, i ll apply for grad school. but am i gonna get fucked?

>>8970914
you think it be like it is but it dont

http://www.themathpage.com/atrig/inverseTrig.htm

for clarity, when you're looking at what appears to be sin x raised to the negative power 1, it is usually referring to the arcsin function. It is for good reason that people say arcsin and not sin(x)^-1

>>8963394
Check out the Carmichael function, it's the replacement for [math]\varphi(n)[/math] to get you the minimal version of Euler's theorem.

https://www.youtube.com/watch?v=3d6DsjIBzJ4&list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr&index=11

most useful explanation of wtf a taylor series is (more advanced than AP calc BC)

Good night /math/.

>>8971300
See you tomorrow.

>>8971300
>/math/
It's /mg/ you dummy.

I'm an idiot. I won't bother you with the whole story but I've basically got 4 days to study an entire syllabus worth of micro- and macroeconomical graphs, market analysis, formulas, functions, etc.

That even possible, /mg/?

>>8971671
>That even possible, /mg/?
Not if you're here instead of studying

go get some coffee, a classmate, and go to the library

>>8971672
Don't even know where to start, senpai. I used to be big into science and math but I went into Law despite getting an okay for medschool and being advised to go study engineering. I just can't wrap my mind around this stuff anymore. Feel like part of me died to be honest.

>>8971671
>That even possible
Yes. I learned a whole semester worth of ordinary differential equations in just one night. Got a 9/10 mark on the exam off it.
But to you? No. I'm way above average in intelligence.

>>8971702

on the unlikely chance that you're not bullshitting, what book/material did you use?

>>8971717
Coddington and I looked over a colleague's seminar notes to get an idea of what sort of exercises I should expect. I started reading at about 17:00 the day before the exam (making notes of proof sketches) and continued doing it through the night.

>>8962452
I grow my own activated almonds

>>8971676
>I just can't wrap my mind around this stuff anymore.
What exactly are you having trouble with?

Proof by mathematical induction that the Pythagorean Theorem can be demonstrated not just with squares constructed from the sides, but with any regular polygon with $n$ sides.
The area of an $n$-gon is defined as
\begin{displaymath}
\frac{s\cdot n\frac{s}{2 tan\frac{180}{n}}}{2}
\end{displaymath}
where $n$ is the number of sides of the $n$-gon, and $s$ is the lengths of the sides.
\begin{enumerate}
\item Demonstrate true for $n=3$.
\begin{enumerate}
\item $(\frac{a 3\frac{a}{2 tan\frac{180}{3}}}{2}) + (\frac{b 3\frac{b}{2 tan\frac{180}{3}}}{2}) = (\frac{c 3\frac{c}{2 tan\frac{180}{3}}}{2})$

\item Multiply though by 2. $(a 3\frac{a}{2 tan\frac{180}{3}}) + (b 3\frac{b}{2 tan\frac{180}{3}}) = c 3\frac{c}{2 tan\frac{180}{3}}$


\item Simplify. $\frac{3a^2}{2tan\frac{180}{3}}+\frac{3b^2}{2tan\frac{180}{3}}=\frac{3c^2}{2tan\frac{180}{3}}$

\item Multiplying through by $\frac{2 tan\frac{180}{3}}{3}$ gives $a^2+b^2=c^2.$
\end{enumerate}

\item Assume true for $n$.

\item Demonstrate true for $n+1$.
\begin{enumerate}
\item $(\frac{a (n+1)\frac{a}{2 tan\frac{180}{(n+1)}}}{2}) + (\frac{b (n+1)\frac{b}{2 tan\frac{180}{(n+1)}}}{2}) = (\frac{c (n+1)\frac{c}{2 tan\frac{180}{(n+1)}}}{2})$

\item Multiply though by 2. $(a(n+1)\frac{a}{2 tan\frac{180}{(n+1)}}) + (b (n+1)\frac{b}{2 tan\frac{180}{(n+1)}}) = c(n+1)\frac{c}{2 tan\frac{180}{(n+1)}}$

\item Simplify. $(\frac{a^2(n+1)}{2 tan\frac{180}{(n+1)}}) + (\frac{b^2(n+1)}{2 tan\frac{180}{(n+1)}}) = (\frac{c^2(n+1)}{2 tan\frac{180}{(n+1)}})$

\item Multiplying through by $\frac{2 tan\frac{180}{n+1}}{(n+1)}$ gives $a^2+b^2=c^2$.

\end{enumerate}
\item Therefore, for a polygon of any number of sides, the area of a regular polygon with sides of length $a$ plus the area of a regular polygon with the length of side $b$ will equal the area of a regular polygon with the length of side $c$.

>>8965983
Am I supposed to look at this left to right or up to down or?

>>8971717
probably just babby's first ode course. You know, char eq., int factors, separation, etc.

>>8966110
Damn that's good though. I was thinking some determinate(left diag, then right) of every block or so. I came up with an answer based on the patterns of similar blocks but there wasn't any way that it was valid.

>>8971808
See >>8971768
Not everyone is a semen slurper like you.

>>8970841
Applied Abstract Algebra

>>8971821
This is funny because Coddington is the very definition of babby's first diff eq. course.

>>8971828
Not that it matters but almost no one recommends Coddington as an introductory book for ODEs.

>>8971833
Except for numerous stackexchange suggestions, and by professors who use it for their textbook of choice.

>>8971842
Professors use it as a guideline around which they structure their course because it's a very thorough and rigorous book, but they usually recommend other textbooks for their course (besides their own lecture notes), and when they do recommend Coddington, they almost always qualify it as additional reading material.
>stackexchange suggestions
reads to me like you have no clue.

>>8971858
not in my experience, bud.

>>8971881
Well, I'm a TA and I'll be damned if I ever saw someone do it or if I'll ever recommend Coddington as a primary textbook to a first ODE undergrad course myself. It's too dense. * marked. For brainiacs and grad students.

I just heard that British and American systems use trillion as different quantity. So, do most people prefer use British trillion or American one?

>>8971918
This is the math general faggot. Use your search engine of choice for such stupid questions.

>>8971157
>>8971158
>>8971182
>>8971300
>>8971505
>>8971305
>>8971671
>>8971672
>>8971672
>>8971676
>>8971702
>>8971717
>>8971768
>>8971772
>>8971775
>>8971797
>>8971808
>>8971810
>>8971821
>>8971826
>>8971828
>>8971833
>>8971842
>>8971858
>>8971881
>>8971896
>>8971918
>>8971947
please help me, dont ignore me
>>8971156

>>8971961
Another stupid question. How the fuck should I or anyone else here know how well you'll do based on your choice for courses next semester? Did you even think before you posted that sausage of quoted posts? We can't read your mind, dickhead.

>>8971961
Posts like this are the reason, why career advice is not allowed on /sci/.

>>8971970
so u think my coursework is ez?

>>8971991
your question is stupid, and vague.

>>8971896
aww baby, someone doesn't agree that you are a brainiac. poor u

>>8971996
i think u might be autistic

>>8971996
What?

>>8962385
Question: Is every complete, totally ordered field with the same cardinality as [math]\mathbb{R}[/math] necessarily isomorphic to [math]\mathbb{R}[/math]?

>>8972065
You also need that every subset has a unique sup/inf.

>>8972065
obviously.
>>8972078
that's what completeness means.

>>8972078
Is this equivalent to requiring it be a Hausdorff space?

>>8972065
Wikipedia says so.

https://en.wikipedia.org/wiki/Ordered_field
>Any Dedekind-complete ordered field is isomorphic to the real numbers.

Trying to learn Fourier transform, DFT, FFT, Coherence functions, Windowing, Filters, and Wavelets, any good resources? Lecturer spent entire time reading theory from powerpoints with no examples, help!

>>8972091
No.

>>8972140
"A wavelet tour of signal processing: The sparse way" by Stéphane Mallat is a good resource, but I don't know if it's suitable for undergrads (which I'm assuming you are since you don't already know about FT/FFT). Having a look won't hurt, though.

>>8972091
A simple counter example:

Consider the ordinary ordering on [math]\mathbb{R}[/math], and define a set to be open if it is of the form [math](-\infty, r), r\in\mathbb{R}[/math], empty, or the whole set. This gives you a non-Hausdorff topology, but the suprema are unique because of the ordering.

>>8967610

It was a quick way to estimate time consuming multiplications fairly accurately and quickly, but you needed a logarithm table for it.

https://qedinsight.wordpress.com/2011/04/22/a-practical-use-for-logarithms-part-2-how-we-multiplied-large-numbers-40-years-ago-and-how-integral-transforms-use-the-same-basic-idea/

>>8967525
what's the actual name of the Fujikawa book

>>8972369
Path Integrals and Quantum Anomalies.

Does there exist an elliptic curve [math] E/\mathbb{Q}[r] [/math] such that specializing [math] r [/math] to a natural number gives [math] rank_\mathbb{Q}(E)=r [/math]?

>be already on the dept mailing list of the uni I'm going for a PhD at
>get notices of really interesting talks and workshops over the summer conducted by the faculty there that I won't be able to attend

Is there a 'visual' interpretation of the Hodge conjecture (in the lowest dimensional case I guess), or is it all algebraic?

What would be the best way to exploit RSA if you managed to find a weakness in the cryptosystem?

What's his endgame?

>>8972951
Which one is that? Come on, dox yourself.

>>8973165
She's already mentioned it before, you new here?

>>8973171
>she
(male)?
>you new here?
1.

>>8972588
>>8972975
>>8972982
Please get a trip so I can filter you.

>>8973180
You can filter filenames, enjoy!

>>8971896
>I'm a TA
At which university? Come on, dox yourself.

>>8973177
>(male)?
What?

>1.
What?

>>8966410
It's a valid sketch of a proof.

>>8973189
Are you going to dox yourself or not?

>>8973194
>Are you going to dox yourself or not?
Why would I do that?

>>8973185
That's too general. I was thinking of writing a script with calls to some image recognition API that hides every post which return "gorilla". But getting the fag to use a trip is easier.

>>8973197
For fame and glory?

>>8973198
I haven't tripped for years, sorry to bust your bubble!

>>8973202
How would doxxing myself give me fame and glory?

Fuck off gorillaposter. I don't want you doxxed, I just want you gone.

>>8966157
Probably because he realised a bunch of shitposters are smarter than him.
>get accepted at cambridge
>get shat on

>>8973216
>Fuck off gorillaposter.
I make better posts than you.

>I don't want you doxxed, I just want you gone.
Unlikely.

>>8973221
Are you implying it's hard to get into Cambridge?

>>8973226
Are you saying it's not?

>>8973512
I got in and I'm a gorillaposter, what does that tell you?

>>8973525
That you're lying.

>>8973553
It's really not that hard to get in my friend

We need a drawfag lmao.
>she
Rofl.
>>8973171
I've said where I am at the moment but not where I'm going for a PhD.
>>8973556
Dude you accepted? Isn't rent expensive as fuck there? How much are they offering you?

>>8973556

>>8973569
>I've said where I am at the moment but not where I'm going for a PhD.
Am I mixing you up with someone else? I thought you said where (don't want to expose but it ended with -er?)

>Dude you accepted? Isn't rent expensive as fuck there? How much are they offering you?
No I didn't accept (that was for master's, says 2015 in the pic) [unless I'm mixing you up I was doing research a couple buildings away from you]

>>8973578
> (don't want to expose but it ended with -er?)
Probably forgot I said it then.
> (that was for master's, says 2015 in the pic)
I thought you were still an undergrad for some reason lmao.

>>8973204
Simple really. In case you ever come up with a cool result, /mg/ will know it was you and will sing your praises for all eternity.

>>8973588
>I thought you were still an undergrad for some reason lmao.
Because he makes retarded posts? Fucking gorilla.

>>8973588
>I thought you were still an undergrad for some reason lmao.
RIP
How much longer till you fly out?

>>8973589
I'll hide the word gorilla for you in the TeX file if I ever come up with a cool result

>>8973604
Probably around mid August. Making living arrangements at the moment.

>>8972588
Unlikely. Why are you asking?

>>8973216

https://www.youtube.com/watch?v=dVVZaZ8yO6o

>>8973615
>filename
whew

>tfw craving that cheap food court but don't want to bus all the way to campus

>>8973617
Plain curiosity since it's obviously unknown, I suppose it would be better to start looking for [math] E/\mathbb{Q}[r] [/math] such that for all [math] n\in \mathbb{N} [/math] there's some [math] m \in \mathbb{Q} [/math] that gives a specialization of [math] rank_\mathbb{Q}(E)=n [/math].

I think the max rank ever found is only like 14 anyway :/

>>8973578
>don't want to expose
>I was doing research a couple buildings away from you
You're just lying to bust my balls because you think I'm out to prank you. Am I right?

>>8973642
>You're just lying to bust my balls because you think I'm out to prank you. Am I right?
No, what is it you think I lied about? (I didn't)

The girl I was responding to already knows where I do my research.

I said I didn't want to expose because she didn't name the school herself

>>8973651
>what is it you think I lied about?
Where she (male) did her (male) master's.
>I didn't want to expose because she didn't name the school herself
I think you're a pussy who's scared he's going to get pranked with pizzas at his office.

>>8962580
lmao this fag doesn't even know how to math text.
isn't this true for infinite products as well?

>>8973690
>Where she (male) did her (male) master's.
But I never even said which, unless you mean lie by omission?

>I think you're a pussy who's scared he's going to get pranked with pizzas at his office.
I don't have an office to send pizzas to anymore, renovations going on

>>8973699
Who's Brian?

>>8972951
Feels bad man, what topics specifically? Also surprised you're not even a PhD student yet, most undergrads never get close to proper qft.

>>8972951
So you endlessly talk about all of that TQFT shit and you're not even a PhD?

Sweet fucking Jesus Christ.

WHERE'S THE NEW THRÄD???

>>8974193
that's really inspiring actually

>>8974211

>>8974800