Hello, I am working on a problem and eventually got this: wolframalpha.com/input/…. I need to know how many integer solutions for x exists (I don't care what they are). Is there any way to mathematically get the answer that Wolfram got (there are 3 integer solutions)?
it's been pretty interesting! the first semester things were a bit slow, I "wasted" some time on some core courses, but the last few months have been very productive.
I've been learning some hodge theory, some characteristic classes, some bona fide algebraic geometry and some other odds and ends.
I recently learned a proof of Chern-Gauß-Bonnet, which I was pretty happy about.
My favorite Gauss-Bonnet proof (without boundary) uses independence of connection and reduces to submanifold of $\Bbb R^n$ and uses Grassmannians and what Schubert cycle the Euler class is dual to.
There's a purely probabilistic proof of Chern-Gauss-Bonnet that I would like to eventually understand; the notes I am supposed to read it from is in the back burner
what is the situation like in india? actually I'm doing a DRP with a cornell undergrad who is in india rn, but he doesn't seem to have a good idea for how it is there
yeah I think basically the idea for surfaces (so just Gauss-Bonnet) is a Brownian motion gets trapped for a long time if a certain part of the manifold is positive curvature, and escapes quickly if a certain part is negative curvature - so you should be able to read off total curvature by running a BM on a surface for a long time
tbh I learned CGB mostly because I think it's a beautiful result lol, I don't think it will be useful for me, but maybe I should learn Atiyah-Singer someday ;)
I got stuck again. Is there some kind of thought process I'm supposed to be having for solving the inequality? I got wolframalpha.com/input/?i=%28%28p%5E2*q%5E2%2Bpq%2B1%29%28r%5E2s%5E2%2Brs%2B1%29%29%2Fpqrs%3E%3D81. Also, I see that some of the solutions have for example r<0, so I'm guessing that means that my bound was too weak?
what about instead of p,q,r,s - try to formulate the analogous problem for only p,q - can you solve it? If not, can you solve a more simplified version?
I think I got it. It ended up being just to prove p+(1/p)>=2. Just to make sure, since the inequality is symmetric, then after I just prove it for p, the others follow by the same argument right?
@Pig Thanks for your help btw. Doing the analogous problem for just p really helped.
I've confused myself about some linear algebra, if I have $\Bbb{R}^2$ with the standard (1,0) and (0,1) orthonormal basis and I use this basis to label vectors by their components, I can label the vector say (2,2) by it's components in this basis. If I then double the length of both basis vectors the components are now (1,1), but these components are relative to the components in the original basis, which I chose arbitrarily and labelled as having unit length?
I'm not trying to be rude, but it would be easier if you looked them up and asked if you have a specific question about a word or phrase being used than just asking for a blanket definition
if you just want introductory stuff you should look for the standard highschool textbooks, if you want undergraduate material you'll have to be more specific than just chemistry
@Charlie I am not really interested in chemistry unlike Mathematics, Physics and philosophy but I'd love to finish undergraduate chemistry since I'd be doomed when I don't understand it well.
chemistry can actually be pretty nasty conceptually
arguably more frustrating to learn than physics or maths since quite a lot of information has to be taken on truth before you can attempt to understand it
no as in if you want to learn about a specific area of chemistry I'll recommend you the textbook I used, but that will depend on the topic, you won't learn organic and inorganic chemistry in the same textbook generally for instance
Group theory is one of the most aesthetically pleasing subject I have ever intersect with so I will choose number theory as my field to study as an autodidact.
Just need some tips&tricks from those who study number theory as a graduate student or a professional number theorist to save time learning this topic.
@EdwardEvans Well it is related with abstract algebra but it is also related to number theory.
Just make sure you learn things thoroughly, otherwise youll end up having to go back and learn some basic stuff before you can continue (i am in this position and its a time sink)
Also delete your account on this site, its a massive time waster
@EdwardEvans No! It's a good place to be where experts like you can give me tips something more related to experience and also good place to ask dumb question.
Well I am not expert. I'd better keep my mouth shut.
Good night. I will sleep instead of wasting time here. See you all at morning if I'll be able to survive this night.
Ok I'll be serious.
$\ln(x^2-8x+1)(x^2+2x+1)=0$
well here you go your exponent is slated by me.
You can let one of your multiple get killed by that 0.
$\ln(x^2-8x+1)=0$
or $x^2+2x+1=0$
Why do I feel this problem is a trap to get roasted XD.
I mean I will again get roasted for answering this question lol.
Will I get suspended if I chat like this BTW good night. Hey I challange everyone to flag my chat right now. Lemme see if you can get suspended for just higher flag. I am testing if it is A.I which decides to suspend you or the moderator.
Can anyone tell me how to compile the latex in chat visually or otherwise I feel attacked for answering answers. Just do visual steps for android!
@EdwardEvans Yes you were right that this chat is kind of good procrastinator software.
Hi everyone, maybe I should ask this a question but want to try my chances here, because it's very short, would be really great if someone can say "no everything is correct in the book" or "you're right": In the proof of Prop2.2 in Jardine's Simplicial Homotopy Theory, while trying to prove that the map is a monomorphism, is there an obvious typo? Namely shouldn't we use the inverse of the $\Psi$, especially because we can't know if the "components" of $d^{*}(x_{\sigma})$ are degenerate or not
I was surveying some literature related to Fully Convolutional Networks and came across the following phrase,
A fully convolutional network is achieved by replacing the parameter-rich fully connected layers in standard CNN architectures by convolutional layers with $1 \times 1$ kernels.
I ...
Hello! Anyone here knows the "easiest" proof(requiring least pre-requisites)to the theorem that The number of ways in which an integer can be expressed as sum of square of two integers is 4(d_1(n)-d_3(n))
Please forgive the lack of rigour in the statement,I know only basic number theory.
I made an aperiodic point set on a disk and wanted to figure what symmetries are present.
By inspection it looks like the points have 8-fold rotational symmetry.
Someone said there might be some hyperbolic symmetry present.
So what is this pattern called and what are the symmetries of the point...
I think my brain is fried today. I spent most of it manually creating payments in a CRM system because of a software error that had caused the system to not do so itself
You would think people would try to pay at most twice when it does not go through but does not give an error. Or at least check if the money is getting transferred from their account.
But there were people who had tried 10 times within 30 minutes
it appears I have to figure out whether $\{(x,\sigma x)\colon x\in\mathbb{C}^n,\sigma\in S_n\}$ is a closed submanifold of $\mathbb{C}^n\times\mathbb{C}^n$ to start with
I spent 20 minutes finding complicated explanations for what the sheaf $\mathcal{F}^*$ might be, when there was already a sheaf $\mathcal{F}$ floating around. I constructed some exotic explanations before realizing it was just the dual.
It's Voisin's book on hodge theory. She is obviously brilliant. Some parts of the book are a bit confusing, though. There are a lot of typos, too.
There was a "proof" about the Hodge structure of a blowup, which was incorrect in many ways. (the first line consisted of a mis-indexed long exact sequence of a pair) and it only got worse
Hi, I just stumbled across a post https://math.stackexchange.com/questions/3717380/showing-a-function-f-mathbb-r2-to-mathbb-r2-is-partially-and-totally-diffe
but do not have the rep to point out neither answer uses the function OP mentioned in their post. Could someone comment this on the answers?
I was surveying some literature related to Fully Convolutional Networks and came across the following phrase,
A fully convolutional network is achieved by replacing the parameter-rich fully connected layers in standard CNN architectures by convolutional layers with $1 \times 1$ kernels.
I ...
I made an aperiodic point set on a disk and wanted to figure what symmetries are present.
By inspection it looks like the points have 8-fold rotational symmetry.
Someone said there might be some hyperbolic symmetry present.
So what is this pattern called and what are the symmetries of the point...
