/mg/ - Math General: Elliptic Edition

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>>8780532
Heya, /math/

I'm pretty happy today : I just realised that there exist a way to transfer from my school to the most prestigious of the country. I can try to transfer either to the math department or the physics one.

>Math :
>One pre-selection process of looking at your records and motivation
>Written selection exams
>Final oral examination

>Physics :
>Selection process based on your records and motivation
>Oral examination, either in a theoretical subject or in a experimental one.
One of the experimental subject was how to calculate the speed of light using a microwave.

I've one year to prepare for it. Starting now. I think I'll be trying physics.

Sorry for the blogpost, I just wanted to share it. Bye !

>>8780532
My school uses Stewart calculus up until calc 3 (advanced calculus)
Is it brainlet?

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>>8780556

>>8780556
It's just very verbose. It's good for what it teaches, though. Very clear and detailed.

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>>8780532
I find none of your lists points appealing or of special interest. desu.

>Current research?
Have to learn some programming for muh job :/
>Interesting problems?
I'd like to create a list of all the easily constructively verifiable problems among the unsolved problems.
Because if I do something notable, I don't want to pull a Mochizuki

Well, in unrelated points on your question, I posed pic related some time ago
>Anything cool on the Arxiv?
I got too many basic books to read to cruise around much on the arxiv, sadly

What's the most painless way to make drawings in LaTeX ? Especially geometrical curves/tangents/angles and all of that

How do I decide whether or not to switch to math in university?

>>8780532
My knowledge of elliptic curves consists of Ch.4 of Hartshorne. How are they used in cryptography?

>>8780595
What are you studying currently, what year and how old are you ? These are the most important factors I guess

>>8780594
Have you tried ipe?
https://en.wikipedia.org/wiki/Ipe_%28software%29
There's probably more advanced programs that let you do more but this should be fine for relatively simple stuff.

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>>8780761
https://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

>>8780761
djb's algorithm ChaCha20 is ECC

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

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

>>>/wsr/286680

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>>8780795
My school has a course being taught with this book next semester. Have you read it?

>>8781055
only small parts of it, i remember it seemed to have a nice amount of detail to it though, very handy as a reference

>>8780532
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

>>8781141
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.

>>8781152
it was just showing absolute/conditional convergence or divergence
i probably should have practiced more

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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

http://mathworld.wolfram.com/q-PolygammaFunction.html

I'm particularly interested in s=2.

>>8781320
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".

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>>8780532
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?
https://arxiv.org/abs/1411.5684
Low energy Graphene is a WZW model.

>>8781415
>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.

>>8781518
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.

>>8780552
grad student?

>>8781970
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?

>>8782088
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:
https://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?

>>8782575
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.

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>>8782592
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?

>>8781487
>>8782610
go away autist

>>8782770
Thanks for the (You)s

>>8782610

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

>>8780532
>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]

>>8782770

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.

>>8781055
i used that as a reference for a mathematics of cryptography course, nice and concise. I like it.

>>8782825
His contributions are sperm in Latex form. I can feel him masturbating everytime he posts.

>>8782844

The latter.

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>>8782825
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.
>>8782851
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.

>>8782866

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

>>8782986
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"

>>8782639
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.

>>8783027
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.

>>8782510
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.

>>8782575
>http://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.

>>8782770
>stop posting math and physics on the science board
kys

>>8783190
He is masturbating in public rather than posting math/science. I think he's kinda purposefully making this even more abstract.

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>>8783204
>i don't understand this particular flavour of graduate-level math/physics so whatever he's doing is mental masturbation!!

>>8782986
it takes a while but you can train yourself to tune out background noise

>>8783212
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?

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>>8783218
>He's also an animeposter, so that doesn't help his case.
is this your first day on 4chan?

>>8783212
TQFT is a shitty subject

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>>8783204
>>8783218
>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?

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

>>8783224
No. But that's still avatarfagging and sometimes shitposting with guns and clubs, as well as adding to the general smugness and intellectual masturbation.

>>8783233
>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.

>>8783259
>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.

>>8783277
>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.

>>8783233
>his language is completely standard
i dont think so

>>8783304
>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.

>>8783304
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.

>>8783320
>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.

>>8783331
>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.

>>8783329
>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.

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>>8783304
>>8783329
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.

>>8783334
It's really good to know you've got the social skills of a 4th grader.

>>8783341
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.

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>>8783348
o: oh no wow you totally BURNED me DUDE!!1
looks like my post hit a little close to home, faggot

>>8783346
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

>>8783362
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.

>>8783356
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.

>>8783364
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.

>>8783374
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.

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>>8783308
Please explain and ask where my language had been confusing. I'm glad to help.
[math]\mathcal{laughinggirls.png}[/math]

>>8783362
This exercise is from Aluffi, right? Good'ol time :'

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>>8783459
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

>>8783440
I didn't say it was confusing, I said it was not standard TQFT.

>>8783464
Looked like a completely standard presentation for an exercise to me. Granted I don't know shit about physics.

t. mathfag

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>>8783464
Who are you to say what is or is not standard? You don't even understand half the shit that's going on here.

>>8783459
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?

>>8783472
I am not the same person you have been aruging with.

I mean this picture >>8783472 and this picture >>8782610 look like standard TQFT. But this stuff >>8781487 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.

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>>8783491
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.

>>8783505
>if you knew some differential geometric/topological formalisms of QFTs

A regular QFT is still a monoidal functor.

>>8783474
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

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>>8783663
tfw we can't have a single thread without at least one anime spamming autist causing at least one flamewar

>>8783080

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

>>8783852
People have more problem with autists complaining about animeposting than animeposting.

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

I'm trying to do this
https://www.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?

>>8785578
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?

>>8783852
It were my fault. I should have backed off and let him post his stuff. After all, jerking off never killed anyone.

>>8783663
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.

>>8785789
>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.

>>8785728
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.

>>8786091
I'm confused, he said himself that he is a mathematician. Whatever.

Next fall i am probably going to take the honors abstract algebra series and honors real analysis series, as it's recommended for grad school. But I heard these courses are balls hard. Should I not take them together?

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>>8786286
I have literally never said that lmao. Did you confuse me with another animeposter? Maybe I should trip so that you can filter me and this whole autistic fiasco wouldn't happen again.

>>8786329
Here : >>8783385

I'm (partly) the one to blame for the autism fiasco, so no need to trip. Just try to explain more, sometimes. If you would.

>>8786308
what exactly do you mean by honors x series? are they the classes grad students are required to have finished or just some undergrad classes? if they're the grad classes i wouldn't recommend taking any other classes at the same time as those two

>>8786347
By "no need to trip", I meant that I won't try to argue with you anymore since there's practically no point.

>>8786347
I'm the mathematician. I didn't post the anime physics image. I said it in the post that I don't know shit about physics, I'm just mad at the other guy shitting on Mr. Anime because he (the other guy) literally didn't know what he was talking about and should stop posting forever.

>>8786308
In my experience "honors" bullshit is a bad meme. But typically first algebra and analysis courses tend to be difficult to students who don't have any prior background in proof-based maths courses due to their rigor (if well-presented). If you're confident, there's nothing wrong with taking them both at once. But if you've never written a proof and/or never been experienced to real, proof-based mathematics then I'd suggest against it unless you study beforehand. Some good references are Rudin (for real analysis) and Aluffi (for algebra; best intro book for algebra imho), though you could probably just ask the professors what books they'll be using and read them beforehand.

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The notation's fucked up, because I had to make some of it up, but I proved that it's importable to see around a corner.

Did anyone study partial differential relations a la Gromov by chance? I'm having some difficulties in general with the various h-prinicple stuff, and that's a huge understatement.

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>>8786347
Contain your autism.

>>8786351

They are undergraduate courses. My uni (UCSD, if curious) has two series for real analysis and abstract algebra. The "rigorous", proof based >>8786389
version which is supposedly equivalent to an honors level course elsewhere, and a non-rigorous version. It's recommended that those looking at grad school take the rigorous versions of the courses. This is undergrad.

>>8786389

Sorry I messed up my post, on phone.

We use baby Rudin for real analysis and some obscure book for abstract algebra. The pre-req is a "Mathematical Reasoning" class which teaches rigorous proof, so I should have some exposure as I'm taking that class next quarter

>>8786545
then i'd say go for it if the rest of your classes are fairly lax
if you're still in doubt just start reading ahead before the class starts so you can at least be familiar with the material before it's presented and that way it won't be such a huge shock

depending on how good that obscure book is i would suggest finding a copy of Aluffi (you can find pdfs online, and the book is available on amazon) to supplement your class text

if your algebra class doesn't cover categories then you might want to slightly skim chapter 1 rather than dwelling on it for too long

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>>8786457

Here I simplified your proof. You can thank me later.

>>8780532
>Daily reminder that elliptic curves are _the_ best mathematical objects.


Don't forget HMS is proved for them. i.e. There is a equivalence between their algebraic geometry and their symplectic geometry

>>8786457
You turned a simple, straightforward geometric proof into some sort of inelegant, needlessly convoluted garbage. Now you're thinking like Pajeet.

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>>8786752
>Don't forget HMS is proved for them.
and the Hodge conjecture!

>>8786457
so THIS is the power of international graduate students in math

>>8782610
>physics problem

>senior year, last semester
>already got into grad school, so don't care about GPA
>take first pure math class ever in chaotic dynamics
>absolutely the least qualified person in the class (only like 10 people)
>midterm comes around
>spend like 1 hour reading the textbook to study
>get a 70, class average 50
feels okay, man

Was there a fifth issue of Acta Mathematica Sinica in 2003? I can't find it.

>>8781320
My thought was to take [math]q = \frac{1}{x}[/math] such that the sum is equal to [math]\sum^{\inf}_{n=1}\frac{x^{2n}}{(1-x^n)^2}[/math] Now this converges when [math]|x| < 1[/math] so I used a taylor expansion which simply gives
[eqn]\sum^{\infty}_{n=1}x^{2n} \sum^{\infty}_{m=0}(m+1)(x^{n})^{m} = \sum^{\infty}_{n=1}\sum^{\infty}_{m=0}(m+1)x^{n(m+2)} \\ = \sum^{\infty}_{n=1}\sum^{\infty}_{m=2}(m-1)x^{nm} \\
= \sum^{\infty}_{k=1}\sum_{m|k}(m-1)x^{k} \\
= \sum^{\infty}_{k=1} \left(\sigma(k) - \tau(k)\right)x^k[/eqn] where [math]\sigma(n)[/math] is the sum of positive divisors of [math]n[/math] and [math]\tau(n)[/math] is the number of positive divisors of [math]n[/math].
So the Laurent solution to your problem is [math]\sum^{\infty}_{k=1} \left(\sigma(k) - \tau(k)\right)\left(\frac{1}{q}\right)^k \equiv \left(\frac{1}{q}\right)^2 + 2\left(\frac{1}{q}\right)^3 + 4\left(\frac{1}{q}\right)^4 + 4\left(\frac{1}{q}\right)^5 + 8\left(\frac{1}{q}\right)^6 + \dots [/math]

Have a look at what closed form solutions equal this in the mean time

>>8788257
I'm not the poster of this problem, but nice try I must say! I tried it for e few minutes by myself, whitout progress.
Although, the very first step, I don't see how your taylor expansion is correct, around what point is it?
This problem reminds me of the Zeta function, not sure if it is easy solvable. What are it's origins problem-OP?

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Good textbook on fractal geometry? Besides Mandelbrot.
Please let it be not very entry-level. Also Yale course online seems to be too retards-oriented.

>>8783027
primes grow like x^1.5 or so. fibs grow 1.6^x. You're really pushing hard...

Just finished my proof of Fermat's Last Theorem. Wiles really overcomplicated things... although his results were very important in other areas too of course. But Fermat only needs a pretty simple logical leap and took more like 7 hours over 3 days, not 7 years.

This is probably the proof Fermat had, or very close... it doesn't use anything that wouldn't've been understood in his time and it's only a few pages (or will be when I finish typesetting the fucking thing. Fuck latex)

I tried writing up a summary but it exceeded the 4chan post character limit. I'll let you guys know when it's ready.

>>8789772
Good job, bro, be sure to keep us posted.

I'm a bio major who is interested in studying math again in my spare time. I only took up to calculus 2 a couple years back, is there an MIT opencourseware you would recommend I take next?

https://ocw.mit.edu/courses/find-by-topic/#cat=mathematics&subcat=calculus

I was thinking "Calculus with applications" but I'm not sure

>>8789799
Multivariable is your next one:
https://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/

I would follow this up with Linear Algebra and then Calc IV (differential equations).

>>8789839
Much appreciated, thanks.

>>8788257
After a bit more work, we can prove [math]\sum_{n=1}^{\infty} \sigma(n)x^n = \sum_{n=1}^{\infty} \frac{nx^n}{1 - x^n}[/math] and [math]\sum_{n=1}^{\infty} \tau(n)x^n = \sum_{n=1}^{\infty} \frac{x^n}{1 - x^n}[/math]. If we sub in [math]x = \frac{1}{q}[/math] into the tau equation, we have the formula for the original question where [math] s = 1[/math].

Now the problem becomes [eqn]\sum_{n=1}^{\infty} \frac{1}{(1-q^n)^2} = -\sum_{n=1}^{\infty} \frac{n}{1-q^n} + \frac{1}{\log(q)}\left(\psi^{(0)}_{\frac{1}{q}}(1) + \log\left(1-\frac{1}{q}\right)\right) [/eqn] Now the question is to find that RHS summation.

>>8780556
It's a solid starting point. Once you get through it, move on to Spivak and then to Rudin.

>>8788558
When I said Taylor expansion, I meant binomial expansion of [math](1-x^n)^{-2} = \sum_{m=0}^{\infty} (m+1)(x^n)^m [/math]. From there it's just basic algebra manipulation.

>>8780532
I plan to build my math skills

Here's the books I plan to work through

I am going to start with an

Algebra and Trigonometry (Stewart, Redlin, Watson)

Book of Proof or some other mathematical proofs book

Now should I do Stewart's Calculus Early Transcendentals, or Stewart's Single Variable Calculus

Then do I move on to Tom Apostol's 2 volume book or onto Spivak's? Or either.

Please feel free to suggest any books?

After calculus, should I move onto linear algebra?

Entering my last year my university and i have not done any extra curricular research but have a 3.5 gpa. My coursework is pretty decent and planning to do more rigorous courses and a couple of grad courses next year.

Do you guys think i should apply for grad math programs or any grad school?

>>8790265
are you 13?


>>8790265

>>8790885
>Do you guys think i should apply for grad math programs or any grad school?
apply to grad school if you want to go to grad school, don't go if you feel it's your only options

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What's your favorite regular polytope, /math/?

>>8792420
icosahedron

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Brainlet here, I keep doing this and getting the answer -42 / -18 before simplifying. What in the fuck am I doing wrong? I swear to god I'm doing the stuff in the parenthesis first, then exponent, then multiplication etc etc.

>>8792631
write out your steps brainlet

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>>8792635
12 - 3 (10 + 8) / 9 (-2)
12 - 3 (18) / 9 (-2)
12 - 54 / -18
-42 / -18

>>8792646
since it says -3(10+2^3) / 9 x (-2) i assume you're just supposed to go left to right and do
-3(10+2^3) / 9 x (-2)
= -3(10+8) / 9 x (-2)
= -3(18) / 9 x (-2)
= -54 / 9 x (-2)
= -6 x (-2)
= 18

i would do what you did if it said -3(10+2^3) / (9 x (-2))

>>8792669
Aren't you supposed to do multiplication before division? Or am I missing something in this case?

how hard was a "intro to numerical methods" class in your Uni?

>>8792674
i was taught that multiplication and division usually take equal precedence (as do addition and subtraction) and that you go left to right

these are just conventions though, and that question should have brackets in there somewhere to make it less ambiguous

>>8792681
Holy fuck you're right anon, my whole life is a lie. Thanks, that explained everything.

How do I be prepared for graduate school?

I know I am supposed to take Real Analysis, Abstract Algebra and maybe some topology or geometry, but should I also do a summer REI?

>>8792720
there a shitload to learn and a first course in real analysis and algebra is something extremely basic.

deifnitely do all the REUs you can

>>8789772
Why do you post lies?

Is baby rudin really good for a first book on analysis?

As for my background I've gone through apostol's calculus 1&2, ODEs by tenebaum, advanced calculus by sternberg and loomis, linear algebra with lax and then roman and algebra through maclane and birkhoff.

>>8793053
Yes.

>>8793053
what is baby rudin? Is that the green book? I was about to check it out.

test

>>8793066
rudin's principles of mathematical analysis

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What equation am I looking for lads. I keep getting the wrong answer desu.

>>8793083
what equation did you get....?

>>8793085
T.. t-tw- 2^x = 2-k

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I have a question for anyone who knows anything related to associative algebra, or anything related to complex/hypercomplex numbers of order 4,8, or 16.

I'm currently a sophomore in mech eng, and I'm doing a research project with my math prof from last semester's calc 3. His work is basically trying to discover a solution to the determinants of hypermatrices. So, knowing basically nothing about linear algebra, I am often at a loss with helping him. I have learned a ton about complex number systems and matrix operations, but he is way beyond my level.

However, one of the ways that he is trying to go about showing a possible correct structure for a hypermatrix is to slap a hypercomplex number into it, and find the right multiplication schema that will allow two of these hypercomplex-encoded hypermatrices to multiply out to their correct hypercomplex answer, which will be de-encoded from the resulting hypermatrix (basically what Cayley did to find the Cayley determinant).That is where I come in, I am writing matlab (I don't know mathematica...) code that essentially tests his schemas, and makes it easy for me to test some of my own. Currently, we are testing order 8 hypercomplex numbers, because they are associative(I am still not sure why that matters for proving the schemas), and I am sure we're getting close to finding a proper schema.

To test the schemas, I am running the program through all possible combinations of single hypercomplex imaginary numbers, 64 combinations, and then assembling a multiplication array to see if it matches what we are looking for. The picture included is my latest test.

Does anything about this picture look like it follows a pattern? I can't pick anything out, and I've run out of new ideas to try.

Anyone know some good really advanced linear algebra books?

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>>8793328
does this work?

>>8793328
What do you already know?

>>8793053

No. You should start with a good intro to predicate logic. You'll find more intros to predicate logic if you look for lecture notes on "discrete" math than if you do analysis lecture notes. So "analysis" is just proving things in calculus with predicate logic. The difference is that in math the predicates are called "sets" instead of predicates. It's also the reason there is a suspicious lack of actual functions in set theoretic math, because much like in ordinary philosophy, things just all ready exist, you don't have to make them, you can just pluck them from the vast constellation of your m̶a̶s̶s̶i̶v̶e̶ ̶e̶g̶o̶ imagination. So the actual reason Rudin is so "hard" is because you're actually just doing logic exercises but no one tells you. While obviously, you implicitly use logical reasoning to get the correct results in math, explicitly reasoning in logical notation can be a strange experience at first. If you're comfortable with logic and substitution rules it shouldn't be any harder than applying logic to any other subject. They trick is realizing that you're doing the logic of math and not math directly.

>>8793802
>"analysis" is just proving things in calculus with predicate logic
>Rudin is so "hard" is because you're actually just doing logic exercises
>doing the logic of math and not math directly

While I advocate against using Rudin for pedagogy, this is a gross, and quite frankly disgusting, oversimplification and misrepresentation of analysis or any math whatsoever.

>>8781132
>Kolmogorov complexity

Why is it important?

I want to understand application of derivative
>geometry
>volume
>limits

In addition,

>propability
>percent calculations.

Level would be Calculus 1 ( I guess)

>>8795292
>gross
>quite frankly
>disgusting
>oversimplification
>misrepresentation
>whatsoever

Tell me about the topoi, where did it touch you?

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>read up on powerful methods in physics
>it's fucking boring
>read up on rigorous construction of physical theories
>it's weak as fuck with very little predictive power

>>8797030
Tell me about K theory, why does it wear the mask?

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>>8797108
Haha lol Bane????