/mg/ - Math General: Elliptic Edition

Have you tried ipe?
en.wikipedia.org/wiki/Ipe_(software)
There's probably more advanced programs that let you do more but this should be fine for relatively simple stuff.

en.wikipedia.org/wiki/Elliptic_curve_cryptography

The group structure and arithmetic of an elliptic curve over a finite field just lends itself essentially perfectly to modern standards of cryptography

I haven't spent time on ECC for quite a few years now but Koblitz book is a great intro to this

djb's algorithm ChaCha20 is ECC

If anybody is interested in ECC crypto see this course by the premiere researcher in post-quantum crypto hyperelliptic.org/tanja/teaching/crypto16/ has video lectures

help me /math/, you're my only hope

My school has a course being taught with this book next semester. Have you read it?

only small parts of it, i remember it seemed to have a nice amount of detail to it though, very handy as a reference

CS student
Try to self learn General topology , and current study and research Kolmogorov complexity

i am a fucking brainlet and just failed a test on series.

i barely finished half the test in the allotted time

how do i get quicker? i've always been very slow at math

What was the test about ? Convergence criteria ? If so, practise. If it's on trying to evaluate what a series converges to, you need to learn by heart power series for usual functions and learn to recognise them.

For very "computational" things like Series or calculus, the only mean to progress is to practise.

it was just showing absolute/conditional convergence or divergence
i probably should have practiced more

I'm trying to crack

[math] \sum_{n=1}^\infty \dfrac{1}{(1-q^n)^s} [/math]

e.g. for
q>1
s>=1

For s=1, mathematica gives me the closed form solution

[math] \frac{1}{\log (q)} \left( \psi_{ \frac{1}{q} }^{ (0) }(1) + \log ( 1-\frac{1}{q} ) \right) [/math]
where psi is the Qpolygamma function

mathworld.wolfram.com/q-PolygammaFunction.html

I'm particularly interested in s=2.

dumb frogposter

Tryna prove the inscribed square problem

Why exactly are we supposed to doubt that the inscribed square exists on a general closed plane curve? They're all equivalent to circles. A circle has an infinite multitude of inscribed squares. At what point, during a continuous transformation of the circle into a general closed plane curve, would all these inscribed squares cease to be?
I wish that continuous deformations of a circle were simply defined as "deformations that preserve the property that the resultant curve has at least one inscribable square".

The renormalization technique used for TQFT before was to find a [math]K^*[/math]-valued 2-cocycle [math]g[/math] such that a new space structure [math](\mathscr{B}_{K^*},\mathscr{A})^g[/math] can be defined. This space structure gives rise to a cobordism theory on the [math]\mathscr{B}_{K*}[/math] spaces [math](X,k) \in \mathscr{B} \times K^*[/math], and a TQFT can be constructed such that the [math]K[/math]-modules are quotiented out by the values of [math]g[/math] on the gluing pattern [math]X = (M,N,f)[/math], with [math]g(P) = k \in K^*[/math] and [math]\tau^{g}(X,k) = k^{-1}\tau(X)[/math] whenever [math]\tau(X) = k \tau(M) f_{\#}\tau(N)[/math]. In conventional TQFT the modules are Hilbert spaces with [math]K = \mathbb{C}[/math], and this renormalization corresponds to fixing a gauge such that the action transforms [math]S'(A') \rightarrow S(A) + \Gamma(A)[/math] in such a way that [math] \Gamma(A) \propto n \in \mathbb{Z}[/math]
>Current research?
I have been trying to extend the category theory treatment of topological superconduction to fractional Hall effect and to find a correspondence between my supervisor's AdS/CFT holographic approach. The subtlety lies within the quantization of the gauge group [math]SU(2)_{\mathbb{C}} = SL(2,\mathbb{C})[/math] to the modular group [math]SL(2,\mathbb{Z}[/math], and the gauge transformations between Hall states satisfies a certain duality whose degeneracy Landau level labels satisfy a Diophantine equation [math]ab + cd = 1[/math] (this is what the holographic approach is based on). If I can reproduce such a duality from the categorical point of view, then this could serve as evidence for a new kind of classification for strongly-correlated systems of fermions.
>Interesting problems?
Prove that Graphene is fucking cool and anyone who says otherwise can fuck off.
>Anything cool on the Arxiv?
arxiv.org/abs/1411.5684
Low energy Graphene is a WZW model.

>At what point, during a continuous transformation of the circle into a general closed plane curve, would all these inscribed squares cease to be?
Deformation does not preserve distances or angles.
If you deform a circle in any manner at all other than a uniform dilation your inscribed squares are no longer squares and you need to find a new one.

Yes, but the squares don't vanish when the deformation occurs. The squares move. They do not move continuously, but they move. The squares rotate, translate, and dilate, as the curve deforms, but they aren't deleted.

If only it were simple to prove this.

grad student?

Kind of. I'm in 3rd year and will be passing the test in 4th year. If I pass, I starting back at 4th year, so grad level.

If I get into the school, I'll litteraly get paid for studying.

Hey, /math/. Was wondering what you guys think about Mathematical Finance / Financial Math. I'll be starting a Masters and progressing towards a PhD this fall. Any cool introductory books on the subject? Any interesting problems/research topics?

How can you start a Masters programme if you don't even have a basic understanding? Assuming you have a Bachelors in mathematics, you could try the following:
people.math.ethz.ch/~jteichma/lecturenotesfinance20141118.pdf

For more advanced reading you can try looking up Malliavin calculus.

How do I develop a better understanding of statistics?

The whole subject to me feels like just pattern-matching the correct algorithm to the given problem without any nuts-and-bolts grasp of what I'm actually doing.

How to git gud at solving math and physics problems?
Any reccomended book?

What's your background? If you're studying natural sciences and only got some handwavy crash course you can always read a statistics book intended for mathematicians. The math itself is fairly easy and should not be a problem.

Landau-Lifshitz

I feel like my schooling left me with a poor understanding of the fundamentals of mathematics. I've taken Calc1-3 and some other classes but I still have this constant feeling that I don't know about some very fundamental things, or rather that I haven't internalized them to the point where everything is intuitive. What's some good, clear, fast reading to nail those down? Also is there some sort of reference for how various topics are related, so that I can get an idea of what I should know before I start looking into advanced topics independently?

go away autist

Thanks for the (You)s

What happens if [math]T_{\mu \nu} \neq \frac{\delta W[A]}{\delta g^{\mu \nu}}[/math] ?

>anything cool

This is kind of cool I guess. Was reading Fermi's thermodynamics and noticed that the degree of variability is the same equation as the Euler's polyhedron formula.

Euler's polyhedron formula:

[math]V - E + F = 2[/math]

Degree of variability:

[math]\upsilon = 2 + n - f[/math]

Nah man, nah. His contributions to these threads are good and detailed. I like that he's always posting problems from the books he is reading. It always reminds me to stop shitposting and go read the books I need to read. Also as a hobbyist I enjoy the challenge of trying to read his posts.

i used that as a reference for a mathematics of cryptography course, nice and concise. I like it.

His contributions are sperm in Latex form. I can feel him masturbating everytime he posts.

The latter.

Fuck I misread your post sorry.
>What happens if [math]T_{\mu\nu} \neq \frac{\delta W[A]}{\delta g^{\mu\nu}}[/math] ?
That's the definition for the energy-momentum tensor. You can consider [math]g^{\mu\nu}[/math] as a general infinitesimal coordinate transform.
Wait so I actually didn't misread your post?
The reason it's bad is because physical quantities are meant to be gauge invariant as well as independent of any arbitrary mathematical choices of how you look at the quantity. You can think of this as like changing coordinate systems in classical mechanics, which should not alter the equations of motion and hence the particle trajectories of the system.
The reason that we don't want the quantum action to depend on the compactification radius is similar. Changes in the compactification radius correspond to a conformal transformation, and for CFTs physical quantities like the partition function and the quantum action are required to be conformally invariant.

Thank you.

How can i concentrate when i'm trying to study? My neighbors and family make a lot of noise, i usually wear headpones with rainymood or white noise, but somethings this distracts me too, any suggestions? I'm not american, moving out at 18 is impossible here

go to a library or coffee shop or anywhere else quiet to do work

I want to make "Daily Improvement" routines but with either complex or absurdly impossible formulas to determine how many of X you do in a day (such as pushups).

Does anyone have some examples of pseudo-linear or even parabolic formulas?

Example:
"Every day (X) do some number of pushups equal to the Xth prime number starting from 1"
or
"Every day (X) jog for some number of minutes equal to the Xth number in the fibonacci sequence"

There are a lot of ways to answer this.

If you mean your skill with high school algebra/trig is bad, find one of those doorstop problem books and grind until you're comfortable.

If you're looking to pin down calculus concepts (and you're interested in math) re-learning calculus is a waste. Find yourself a real analysis book. Rudin is the standard but it's very difficult to read for most people; Carothers is a more palatable alternative that helped me during that course. You can pick anything though, it doesn't matter too much.

If you mean actual foundational math as in set theory/construction of real numbers/proofs of very basic algebraic properties sort of thing, you can find that in an appendix to many analysis books. Or you can read Landau's book if you're severely autistic.

If you want some sort of "roadmap" or network of prerequisites look up the math degree requirements on the Harvard website or something. But a better way to approach the problem of "what am I supposed to learn next?" is to find something you really _want_ to learn and then try to do it. If you bump into a wall of prerequisites, go and learn them.
For example, if you're interested in understanding the prime number theorem you will find you need a fair bit of complex analysis to do so; this is a very, very good reason to learn complex analysis, much better than "it's what people do after real analysis."

Just make sure you set reasonable goals rather than aiming to read Mochibazooka's papers.

Generate a random number N between 1 and 100.
Over the next seven days, do N sets of X (insert exercise here) where X is the number of terms in N's Collatz Tree, inclusive.

>roll 16
>do 16 sets of 5 pushups

>roll 27
>do 27 sets of 111 pushups

>roll 97
>do 97 sets of 118 pushups

The unluckiest man will have the strongest arms.

Since we are in topic, does someone want to share a bit of intuition behind divisors / Riemann-Roch theorem? We used it an undergraduate course on elliptic curves (3 CFU) that followed Silverman shittybook, but didn't get it at all.

Because I don't have any background in finance and I spent all my time doing grad set theory and theoretical CS but I thought it'd be a cool field after investigating it on my own time.
Thanks for the rec though, appreciate it.

>people.cs.uchicago.edu/~laci/06dm/lecturenotes.pdf
The probabilities chapter(s) in these notes are the best presentation I've ever seen of the subject. Do the problems on his website (in the course for Discrete Math) and statistics should feel like a breeze.

>stop posting math and physics on the science board
kys

He is masturbating in public rather than posting math/science. I think he's kinda purposefully making this even more abstract.

>i don't understand this particular flavour of graduate-level math/physics so whatever he's doing is mental masturbation!!

it takes a while but you can train yourself to tune out background noise

I'm not against posting graduate stuff. I am against making it sound that way. At least make an effort to explain your rambling.

He's also an animeposter, so that doesn't help his case.

Why are so many mathematicians religious?

>He's also an animeposter, so that doesn't help his case.
is this your first day on Veeky Forums?

TQFT is a shitty subject

>i don't like math/science AND i think he's presenting it in a scary and intimidating way just because i don't understand it even though his language is completely standard and precise
Are you joking, lad?

Can someone pls help me with this problem? Any help would be greatly appreciated

No. But that's still avatarfagging and sometimes shitposting with guns and clubs, as well as adding to the general smugness and intellectual masturbation.

>he's presenting it in a scary and intimidating way
But he is. What's stopping him from dropping a little : "in layman's terms..." or rather a simple "and that helps me with [subject]".
I'm not denying that is a very good scientist/physicist/mathematician, miles ahead of what I am. But what it's worth, he could as well be posting Japanese.

>But he is. What's stopping him from dropping a little : "in layman's terms..." or rather a simple "and that helps me with [subject]".
The fact that no one in the fucking field speaks in "layman's terms" because precision and unambiguity is invaluable in math and the hard sciences. You're the kind of person who wants everyone to dumb themselves down to your level because you can't be assed to learn. Protip: no one fucking cares and you will simply be ignored while the adults discuss what they want to in the language that suits them.

>because precision and unambiguity is invaluable in math and the hard sciences
Poor snowflake, can't bring himself to let go of his precious jargon just for one second.
>You're the kind of person who wants everyone to dumb themselves down to your level because you can't be assed to learn
But I try to learn, I'm just not here yet. Imagine if I was posting in a foreign language in this thread. I could use the same argument as you.
>Protip: no one fucking cares and you will simply be ignored while the adults discuss what they want to in the language that suits them.
Good scientists know their subject well enough so that they can describe it vaguely and have a general idea of what it is like.

>his language is completely standard
i dont think so

>wah I'm mad I can't understand a question that wasn't posed to me so I demand others dumb down their language to my level
>I'll also draw a false equivalence between posting scientific jargon on a science board to speaking in non-english on an english-speaking board
Por favor, comete suicidio. No tienes nada de valor, ni intrínseco ni extrínseco.

It would be completely pointless to present a problem like that to someone who was unfamiliar with the terminology. There really isn't anything complicated about his language, there are just a bunch of big and "scary" terms that only look scary because you don't know their definitions. If you took every noun in the problem and learned its definition there would be absolutely nothing remarkable about the language used.

You're just complaining about not understanding and then demanding to be spoon-fed.

>Hurr durr just kill yourself
Because posting anime girls and random symbols WITHOUT ANY OTHER PURPOSE than showing off REALLY is what brings value to this world.

I'm happy to learn and I think you/he is a great guy. He would be even better he get off his fucking high horse.

>wah I can't understand him so he's showing off!
I'm so glad to know that you'll get nowhere in life and die a failure with no accomplishments.

>There really isn't anything complicated about his language, there are just a bunch of big and "scary" terms that only look scary because you don't know their definitions. If you took every noun in the problem and learned its definition there would be absolutely nothing remarkable about the language used.
Well, then what is the point ? If what you're showing off isn't technically hard, but just hidden being an obscure jargon,, isn't it that just showing off ?

I'm not against mental masturbation if you admit it.

To illustrate: presenting this exercise to a high-schooler unfamiliar with basic algebra or topology would be absolutely pointless. The high-schooler can complain all they want about the scary language but the point is that the only barriers presented by the "language" are the terms unknown to the high-schooler. Anyone with the knowledge requisite for tackling this exercise would either already be familiar with all of the terms and "jargon" or have no problem looking them up for 5 seconds. Anyone who sees these as a barrier should not be worried about tackling this exercise in the first place.

It's really good to know you've got the social skills of a 4th grader.

Do you not know how to read? The difficulty lies in the PROBLEM and NOT in the language. The language is a means to the end of presenting the problem unambiguously and precisely.

o: oh no wow you totally BURNED me DUDE!!1
looks like my post hit a little close to home, faggot

I am aware of how important it is. But really, if you want to share something, at least make it understandable. Otherwise it is simply showing off.

I'll leave it here now, we've got enough autism. I just wanted him to notice that maybe it would be great if he were more explicit. Define some terms of jargon. Trying to share. I guess that'll fall on deaf ears.

>inb4 hurr you want to be spoonfed

It is understandable to anyone who cares about the subject. All you're doing is showing how little you care while demanding to be spoon-fed.
Kill yourself. For real. We'd all be better off.

Well, it didn't really. I'll make what I want. I don't have to "succeed" to be happy. It's sad that you're so intelligent and yet so full of yourself. I though at least a bit of humility was required to succeed in life.

Another kill yourself ?
>showing how little you care
I still care to respect you as a scientist and asking that you explain it a bit.
>It is understandable to anyone who cares about the subject.
Let me doubt that.

I'm not even a fucking scientist you fucking autist I'm a mathematician. The reason I keep telling you to kill yourself is that instead of READING and understanding the criticisms being levied at you you just blame everyone else.
You lack the basic ability to observe and correct your own behaviour. The world would honestly be better off without you.

Please explain and ask where my language had been confusing. I'm glad to help.
[math]\mathcal{laughinggirls.png}[/math]

This exercise is from Aluffi, right? Good'ol time :'

ye boy, best introductory algebra text i've ever read~
hope I can interact with him when I start my grad studies in math at his uni this fall

I didn't say it was confusing, I said it was not standard TQFT.

Looked like a completely standard presentation for an exercise to me. Granted I don't know shit about physics.

t. mathfag

Who are you to say what is or is not standard? You don't even understand half the shit that's going on here.

Also, someone cares to explain the meaning of this exercise? Is it that Spec(C(K,R)) is an extension of K, since MaxSpec is omeomorphic to K itself? Then what good properties has Spec(C(K,R))? It was some kind of completition of K, right? Is there an analogue to Stone representation theorem, where here you have R instead of Z_2?

I am not the same person you have been aruging with.

I mean this picture and this picture look like standard TQFT. But this stuff doesn't, I don't know what you mean by spaces. In everything I have read TQFTs are usually discussed as monoidal functors, not as some spaces.

There is no "standard" TQFT, there is only different notions of TQFT. Also if you knew some differential geometric/topological formalisms of QFTs then you would have seen some semblance or analogy bewteen the "standard"TQFT that you love so much with my "non-standard" TQFT.

>if you knew some differential geometric/topological formalisms of QFTs

A regular QFT is still a monoidal functor.

I think the problem is pretty self-explanatory. It's page 155 of Aluffi's Chapter 0, for reference. From Chapter 3 on Rings & Modules.

i like the other anime poster more than this guy

tfw we can't have a single thread without at least one anime spamming autist causing at least one flamewar

Just got back, this is a nice response and addresses most of my concerns. Thanks a lot.

People have more problem with autists complaining about animeposting than animeposting.

I asked /sqt/ but they weren't any help.

I'm trying to do this
encyclopediaofmath.org/index.php/Geodesic_circle
in Mathematica but to no avail.

I followed along with "Modern Differential Geometry of Curves and Surfaces with Mathematica", though I couldn't use their code verbatim since it was for v3, and ended up with a figure that exactly matched there own (luckily Wolfram hasn't changed the default viewing angle for their 3D plotting in a decade).

Basically what's going on is that from the black point to each red point is a geodesic curve along the torus. The curve joining all of the red points is SUPPOSED to be a circle (all points 'geodesically equidistant' from the black point) but when I integrate for the arc length I get different numbers.

Are there different meanings of "geodesic circle" between authors? Am I doing something wrong with the integration?

Only one definition I ever heard. Picture doesn't look right, but looks can be deceiving. How much difference is there in the arc lengths? Are you integrating along geodesics?

It were my fault. I should have backed off and let him post his stuff. After all, jerking off never killed anyone.

He's a topologist, we have to excuse him.
I'm reading an intro book to it - metric spaces, topological spaces, homeomorphisms, etc. It completely changes the way you look at the most basic stuff, like new definitions of limits and continuity that are much more elegant than the traditional epsilon-delta mechanisms.

>he's not a topologist

no, he's stated this already that he's a physics graduate student who is using topology (and CT) to study supercoductors so that way you can store more porn on your hard drive.

You can see a few of the arc lengths in the bottom right hand corner. The differ quite a bit (2.8 to 5). The integrals are along the geodesics.

I'm confused, he said himself that he is a mathematician. Whatever.