So what do you guys like about math?

Well, guess I am not sending the mail anymore then.

@Nikunj Well, most people here don't talk about math very much.

Probably because the people who do have moved to separate rooms to talk about math.

Oh

Maybe I'll try to generalize the space filling curve argument for maps onto manifolds of higher dimension later. Too sleepy to math.

Guys, how exactly do you show that cartesian product of identical sets is non empty? math.stackexchange.com/questions/23758/… in this question, I don't really get the answer - from what axiom does it follow that the defined function is actually a set?

Well, I suggested to change the name of this chatroom into something specific.

I think mathematics is pretty specific. It suggests that one should be talking about mathematics, unlike me right now, given that I'm talking about people not talking about mathematics.

Haha

I mean, you are talking about maths if you're talking about people not talking about maths, @MikeMiller.

I think I'm talking about sociology.

But people sometimes interpret "mathematics" as lame personal philosophies, which lead to a lot of drama here.

There's no way to misinterpret "Hodge theory"!!

Not an avid fan of the drama.

I guess I'm advertising that I think people should do math here, because I don't want to join other rooms. ;-)

Yeah, the happy memories.

Nah.

The click can be done in time $dt$ but integrate over the days and you've basically spent your whole life clicking 'rejoin'.

All the old crew are gone. AlexGruber, Pedro, Karl. They just show up occasionally.

I'll be gone if Ted and Mike leaves.

Anyway, I gotta go. See ya.

Bye.

That timing.

You already know a lot more than me.

lol, @Khallil.

How are you guys so good at math?

I don't about the universal enveloping algebra crap you talk about.

(didn't mean to say crap in the literal sense. just joking ;))

If you really want to know something I don't, learn Lurie's Higher Algebra.

That's the holy bible.

As a prereq, you need to know topos theory.

A Grothendieck topos is the category of sheaves on a Grothendieck site.

That's all, you now know all of topos theory.

:P

I don't know, because I don't really know what a topos is.

shrugs

Are you really seriously considering to learn higher topos theory??

I'm very serious now : you need a heck of background.

Mostly on algebraic geometry, I'd guess. Not anything like a first course on alg geo.

If it's Lurie, I'd bet you also need algebraic topology.

Plus, a lot of category theory, homological algebra, and all that abstract stuff.

I'd suggest to spend time on something concrete first.

It's highly unfeasible.

Guys, sort of tied to the question of nikunj - how did you get good at math/become genuinely curious about it, as opposed to say playing video games? I mean it's hard to imagine kids willingly choosing to do math, rather than playing some games, and I presume you've been doing math quite a bit in your free time since childhood.

@Jake1234 (Coming from a kid) Learn science. It helps to give a physical interpretation of some concepts. For example, derivatives make a lot of sense when using examples regarding velocity. Talking about vector fields makes more sense when playing around with Newtonian gravity.

Similar with me Alex

@Jake1234 I played video games earlier today.

Also, find friends, who like math/science/whatever. It helps to work and learn and play along kids who want to learn the same things you do. It also makes for interesting conversations at lunch.

Now doing math.

@HDE226868 I get that intuition behind things helps a lot, but all my much younger siblings never wanna do anything like that in their free time.

if math was taught correctly at high school, kids would do math instead of playing video games.

@HDE226868 If there were people in my school who wanted to talk about math/science at lunch, I didn't find them.

And I was in every nerd club.

@BalarkaSen I play video games and do math.

Balarka - I think underestimating how much kids don't want to put effort into things, I know I was like that.

@Jake1234 Give 'em a popular science book. I recommend Michio Kaku. Do make sure that they know what's exaggeration/speculation and what's fact, but give it a shot. Physics of the Future will draw in most kids. Popular science doesn't at all resemble real science, and it avoids math, but it makes people think, and ask questions about the world. Then maybe they'll learn on their own more advanced stuff.

Why must this be mutually exclusive?

@HDE226868 Hey, you're trying to turn kids into string theory instead of math. Not fair.

There's not a lot of difference.

Math and string theory overlap, but it's scandalous to say there's not much difference, imo!

@BalarkaSen The percentage of string theory that I know is infinitesimal.

(e.g., low dimensional topology has physics all over)

@Jasper Ah, but they're one-dimensional. My knowledge is zero-dimensional.

@0celo7 It's not mutually exclusive. But it's hard to find kids who would willingly choose to do math over playing video games or watching tv/youtube.

Not that I'm proud of that; it's simply really, really advanced.

I've never really understood what string theory is all about though :P I just know some of the mathematical formulations.

(string topology, topological QFTs)

@Jasper I'm not sure if I should feel stalked or not...

i dont think if people dont clearify their points in the core of questions, or is it blamed on my misconception

I fear posting a question... because my math-foo is not as strong as it should be... And I'm a bit lost. Mind if I attempt to pose (what is probably) a simple question, and someone could give a nudge?

I am letting a user scale and alter the X/Y of an image... but the display (on mobile device) is also at scale. So, if the display is at 90%, and the user scales the image to 75%... what is the end scale? (so that I could render it later... at some other scale, and honor the 75% adjustment)

crazy enough?

the image is rendered with a bunch of other stuff, so i'd like to minimize rounding errors

and, thank you for any nudge

@BalarkaSen Basically, "The undertaking called string theory started out as perturbative string theory where the idea was to encode spacetime physics in perturbation theory by an S-matrix that is obtained by a sum of the integrals of the correlators of a fixed 2-dimensional conformal field theory over the moduli spaces of conformal structures on surfaces of all possible genera – thought of as the second quantization of a string sigma-model."

That's what most texts start out with.

Hello here.

Anyone could help with vectors ?

@eric concatenating those two scales gives you $0.90\cdot0.75=0.675$

Math question here: Can someone tell me intuitively what$$(a,b,c) \in \mathbb{R}^3\backslash \left\{(0,0,c)\in\mathbb{R}^3|c\in\mathbb{R}\right\}$$means? I'm trying to get a geometrical idea of what it is. All I can think of is that the triplet $(a,b,c)\in\mathbb{R}^3$ except for all points on the line $z=c$. Is that right?

What's a conformal structure?

@BalarkaSen en.wikipedia.org/wiki/Conformal_equivalence

thank you @robjohn

@HDE226868 try using \left\{...\right\} to get better sized braces.

ah, ok. Thanks.

seems so easy...

@robjohn Thanks. I'm not good with using } and { as actual brackets.

I'm not sure why I thought the net adjustment would be greater than .75

@eric it depends on if the scales are going in the same direction or not.

@0celo7 OK, now you have to explain me what a conformal field theory is, because the only kind of qfts I am familiar with are tqfts.

@BalarkaSen Ahh, I haven't looked at string theory in half a year

Lemme get out the ol' BLT (Blumenhagen Lust Theisen)

sure, thanks.

@BalarkaSen Basically, it's a QFT in 2 dimensions that's invariant under the conformal group.

That's the main "symmetry"

@HDE226868 Getting the wrong sized braces can be very distracting to the reader.

Can anyone explain how to find limsup of $\frac{x+a}{x+b} sin^2(\frac{1}{x})$ where a and b are real numbers?$ sin^2(\frac{1}{x})$ will be bounded by $1$ but the fraction behaves weirdly

@Paradox101 where is $x$ heading?

@robjohn Yeah, thank goodness for \left and \right! Thanks again.

Yeah, so the deal is I am not really familiar with what a QFT is. A TQFT, to me, is just a tensor functor from the category of cobordisms of n-folds and the category of k-vector spaces. I don't even understand where the field theory comes in, but I didn't really care when I learnt it because the mathematical results came out fine and physics-independently.

Is there a functorial way to define CFT's too?

@Jasper They inspire, not educate. That's what's needed to get more people interested in science/math/etc. You then need to spend a while correcting the mistakes, but it gets people interested, at least.

Most of those words mean nothing to me.

I have no clue.

@robjohn x will head to infinity?

Urk, oh well. Thanks though.

@Paradox101 then the whole thing will tend to $0$. $\frac1x\to0$ so $\sin^2\left(\frac1x\right)\to0$. $\frac{x+a}{x+b}\to1$

@robjohn how?

@BalarkaSen Ask me in a few years, maybe.

Although I'm more interested in GR.

Definitely :)

Ah, I see.

I'm not a physics major btw.

Just interested.

GR is too geometric for me. I only know a bit of topology.

@0celo7 You're a math major, then?

I'm an engineer so GR is a great way to apply computational methods and PDE theory.

@BalarkaSen Math and nuclear engineering.

ahh.

String theory is tricky because unless you know a lot of physics you'll get lost.

And you need to know a lot of math, of course.

I gave up learning string theory because they never explain any of the group theory and any of the supersymmetric quantum field theory.

I believe you, because everytime I tried to dig into it I came out confused. I just know a few mathematical contexts in which they are helpful to do topology (pretty surprising! math should help physics, not the other way around!)

@Jasper Nah. That's not a part of east-indian culture.

@BalarkaSen Take geometry. Without GR and QFT I doubt we'd have as much geometry and spinor and twistor literature as we do.

@Jasper Not entirely true. Our Diwali is of a different kind, and is called something different.

But I don't care.

@0celo7 Fair enough.

@BalarkaSen And Lorentzian geometry would be unheard of!

@robjohn I don't get it. If we take sin part out of the way as it's bounded by 1, then we're left with the fraction part which will be discontinuous and from the graph x will move towards positive and negative infinity. The how will the whole thing tend to 0? If we take x tends to infinity then the whole thing should tend to infinity no?

I missed the thread about how people got good at math, but lemme say that I owe it all to my awesome dad

Why would anyone want a metric tensor that isn't positive definite without relativity?

who bought me tons of math books

I have a huge bookshelf full of them now

@0celo7 Right, those stuff.

@Paradox101 But as $\frac1x\to0$ we have that $\sin\left(\frac1x\right)\to0$. Remember, $\sin(x)$ is continuous near $x=0$

I have heard of Lorentizan geometry a bit.

Dunno anything.

@Jasper I'm 15.

And he's been doing this since I was probably half that age.

@TedShifrin Geodesic ball time?

(Turning 16 soon)

I've thought and thought and I can't complete the proof.

@robjohn when we're taking limsup we first take sup then limit?

why not, dude?

hi @robjohn

lol

@Jasper I have some meant for kids, like Penrose the Mathematical Cat (or whatever it's called)

Balarka, you were supposed to be in bed hours ago.

@Paradox101 if the limit exists, then both the limsup and liminf are equal.

@TedShifrin Right, good point.

Night!

@Jasper Lots by Ian Stewart, who wrote a bunch of math popularizing books

@TedShifrin wassup?

I can cover the manifold with balls. I can take a finite cover. I can find the smallest radius. But why does this have to be a minimal radius for all points?

I wasn't trying to get that personal, @Jasper.

@Jasper And lots of more technical ones

@Jasper TMI...

@robjohn if i am to approach this problem should i first check the fraction part or the sin part?

I'd be lying if I said I'd read all of them, though.

Because for each point $p$, there is a $\rho$ that works for all points in $B(p,\rho)$, @0celo.

@Paradox101 Both parts tend to a limit as $x\to\infty$ so you should look at both.

@TedShifrin There could very well be a point with a really small geodesic ball, but I cut that one out when building the finite cover.

@TedShifrin Why?

I thought you said that wasn't true. I must have misunderstood you.

That all follows from what we were doing yesterday, @0celo, before you were a rude ass and started calling me dude.

Ooh, he also bought tons of homeschooling videos which I watched with him. Basically how I learned calc. (I'm not homeschooled in anything else, though)

@robjohn so first I need to see how the fraction part behaves? Because only then will I know where x is tending to?

@TedShifrin Rude ass?

Sorry if you think that's rude.

That on top of not listening to what I say, time and time again, it gets on my old professor nerves. Yes.

I am listening to you!

I just don't understand you! Those are two very different things!

So the point was that smoothness of exp is going to tell you (and it's proved in every Riemannian geometry book) that for every $q\in B(p,\rho^*)$ there is a $\rho>0$ (perhaps less than $\rho^*$) so that you get a geodesic ball $B(q,\rho)$.