Mathematics

7:00 AM

Any of you know anything about fractional calculus? It's come up in some papers I've had to read and I can't find anything solid about it.

Besides the wiki, which hasn't helped too much with some things.

Kaj Hansen

lol

Brody

@KajHansen struggle life. but it's rather common in this age with them 'darn techno-gizmos

@Fargle Funny. It's just past 2 am here, and I have to wake up some time before 7. I'll probably all-night it though

Balarka Sen

Ugh

user400188

Deleting an answer doesn't remove the downvotes you received does it?

Kaj Hansen

@Brody, a lot of it was that school was taking up a very, very large chunk of my life, and I felt like I needed time to do things that I was interested in. I did not like school very much at all.

Brody

7:09 AM

@KajHansen I see. so your sleep took the hit, eh

Kaj Hansen

Yeah

user400188

I'v spent the last 3 hours making this answer better but I'm starting to wonder If I should just give up or not.

Kaj Hansen

It shouldn't be mandatory

Mike Miller

@Balarka I slept for five hours but I did get 18 pounds back and so I feel great. Maybe try getting a refund.

Kaj Hansen

I could've passed the GRE in 8th grade.

It's a little infuriating actually, thinking about all the squandered time :/

Brody

7:11 AM

Impressive

thought for food

^

Brody

yeah, they could really work on accessibility to higher-level programs for gifted students

Balarka Sen

@MikeMiller Haha

TheGreatDuck

I think I'm an idiot and that's no joke. You people are sometimes way younger than me and know eons more and yet here I am rambling about nonsense nobody cares about. Perhaps I'm just not meant to be on this community I realize that now. Sorry for annoying you all these weeks and for wasting your time. Goodbye.

Kaj Hansen

Most people feel that way

thought for food

7:16 AM

Don't leave please @TheGreatDuck

Balarka Sen

How did you lose them in the first place?

Kaj Hansen

Most people that know enough to not be Dunning-Krugering themselves at least

Hi chat

Hey there

hey

7:18 AM

Hello

TheGreatDuck

@KajHansen yeah but all I do is ask tings that are inevitably vague and unclear anyway. I have nothing to contribute here.

Fargle

@TheGreatDuck Literally that's exactly how I feel.

Kaj Hansen

That takes practice to improve on

Fargle

Definitely. A big part of the craft of mathematics is learning how to ask the right questions. It just takes time, and asking a lot of questions.

Kaj Hansen

Having experts to interact with in person helps too. I'd be a lot worse off without people like Ted. I really sort of doubt I could've improved anywhere near as quickly alone.

Mike Miller

7:26 AM

@Kaj I don't consider all the time I spent playing video games to be squandered.

TheGreatDuck

Yeah except I occasionally have the uncontrollable urge to just want to rip everything apart. Figuratively that is. I mean, there's questions I ask that get a bit of attention and then I just feel bad for wasting people's time like that.

Mike Miller

In fact, I might play more this morning.

TheGreatDuck

I don't have time for video games. Math is far more important.

Brody

The fact at least three or four frequents in this chat are middle to high school age and know significantly more than me can be inhibiting or it can be motivating. It really is an attitude thing.

Kaj Hansen

Neither do I actually @Mike

Mike Miller

7:27 AM

I find it to be neither @Brody. It just is.

TheGreatDuck

Yeah but I mean this site is only for people who know real analysis. So im not supposed to be here.

Mike Miller

The most inhibiting thing right now is that I don't have my laptop.

Kaj Hansen

Why not?

Balarka Sen

On the bright side you don't have to write

or at least have a good excuse not to

TheGreatDuck

Because only people who know real analysis are supposed to use the site.

Balarka Sen

7:29 AM

I dunno analysis

TheGreatDuck

i was point blank told to either learn it right away or leave.

Mike Miller

I left it at airport security. I'll be able to get it again on a tuesday.

Alessandro Codenotti

Duck feathers, ink and parchments, like the greatest mathematicians!

Kaj Hansen

LOL, what's that all about @TheGreatDuck ? I'm pretty shit at analysis myself. I know the basic dealios behind differentiation, integration, uniform continuity & convergence....and that's about it

Mike Miller

I had an idea I want to work out but I can't exactly find references for related things ::

Kaj Hansen

7:30 AM

My posts are like 40% algebra

TheGreatDuck

@user1952009 told me this site was only for the level of real analysis or higher?

Balarka Sen

@KajHansen Ted is a great teacher. But I am too ashamed to ask my generally stupid questions to him

Kaj Hansen

Me too Balarka :P

Heck, I was ashamed to come to office hours

TheGreatDuck

Idk. It seems lately like everything I do on this site has a negative impact.

Balarka Sen

Ted's just too good at spotting nonsense said by me

Fargle

7:32 AM

@TheGreatDuck Fortunately, that user isn't the gatekeeper of this site. We don't discriminate.

Kaj Hansen

Was perhaps a good thing in its own right though. I was motivated to figure things out myself

Ramanujan

@KajHansen so you are his student?

TheGreatDuck

@Ramanujan ted is retired.

Balarka Sen

@KajHansen Yeah.

Kaj Hansen

I took linear algebra/multivariable analysis and differential geometry from him a few years ago

TheGreatDuck

7:33 AM

:/

thought for food

Did you ace it @KajHansen if you don't mind me asking

TheGreatDuck

Idk. I think I just really need to think about why I'm here. I want to know cr

ertain things and I ask a lot of questions but on the flip side it seems like I just keep undermining myself.

Mike Miller

You really shouldn't be ashamed of asking questions. The job of a good student is to be stupid long enough to learn not to be stupid.

10

But how are you going to do that if you're never willing to be an unabashed idiot?

Kaj Hansen

"Absolutely not" would be the answer for the second semester of that multivariable analysis @thoughtforfood. It got incredibly abstract. Doing vector calc with differential forms instead of the traditional route on very-hard-to-visualize stuff (sometimes >3 dimensions) and got into stuff like proving the Hairy ball theorem & Brouwer fixed point with techniques we picked up.

I did not-horrible in first semester though, and not-horrible in differential geometry. I have a general difficulty with visualizing things though. A lot moreso than most people it seems. I'm very depended on mathe…

Balarka Sen

You're right. I think I really am going to ask him about moving frames today.

It's all very confusing for me.

Mike Miller

7:42 AM

I don't think it's abstract at all! But it does take time to understand it.

TheGreatDuck

I personally like frames on a curve

thought for food

@KajHansen interesting...

Kaj Hansen

I see where you're coming from @MikeMiller. I guess it was abstract for me, someone fresh out of high school and hadn't seen a math course in 3 years

TheGreatDuck

Though I probably have no clue what I'm talking about anyway.

Balarka Sen

@KajHansen I think I am quite good at visualizing stuff because topology is my arena, but I have hard time doing anything with diff. forms, and differential geometry.

Kaj Hansen

7:43 AM

I think it would've been a lot easier had I taken a Spivak-oriented single variable course

Mike Miller

That'll do ya.

Brody

@KajHansen like a transition buffer?

Mike Miller

Ted won't believe me, but I don't like abstraction. You need a reason for everything you do.

Kaj Hansen

There's something called the Frenet frame @TheGreatDuck. Interesting stuff really

Mike Miller

I think any good concept has a clean and comprehensible origin and meaning.

(My usual phrasing for this is: I don't believe in magic.)

SteamyRoot

7:47 AM

Do You Believe In Magic - The Lovin' Spoonful

►

Brody

@Mike reminded me of just that

Mike Miller

Every time I tell someone my slogan I get that song stuck in my head.

Kaj Hansen

Yeah @Brody. For example, Riemann integration in $n$ dimensions is a natural extension of Riemann integration in single variable

Mike Miller

I think if there's ever a rapture, I'm going to find someone else still around and start freaking out: "Everyone's gone! Everyone's gone!"

"Everyone's gone... surfin. Surfin USA."

Brody

Well @Kaj, you took the courses I wish to have taken. I would've loved the more theory-intense courses at UGA, even if they'd kill me

TheGreatDuck

7:54 AM

@KajHansen I know about the Frenet Seret

@MikeMiller that's a horrible joke

Kaj Hansen

That's awesome @TheGreatDuck. Have you looked at any surface theory? That's where frenet applications get interesting

TheGreatDuck

Nah

I just made a half-broken tube plot in the graphics classs

I have not taken differential geometry

im undergrad

Mike Miller

I will be the first person murdered (as opposed to accidental death) as a consequence of the rapture.

Kaj Hansen

Oh? Why's that?

TheGreatDuck

Are you the antichrist or something?

Mike Miller

8:00 AM

I just meant the above joke.

TheGreatDuck

Cause last I checked everyone keeps putting Donald trump on that list.

granted

those people are idiots

Tobias Kildetoft

@MikeMiller Hey, get anywhere on that puzzle?

thought for food

They are the majority.

Like it or not

Brody

God may perhaps smite you Himself for that, @Mike

TheGreatDuck

No I mean the people who literally believe Donald trump is the antichrist

@MikeMiller I'm pretty sure the first murders will be from the serial killers realizing they have nothing to stop them from rampant killing. Honestly I wonder how many people would die solely from the sheer insanity of people flipping out and going on a killing spree.

I'm too cowardice for that. Randomly deleting my favorite posts is enough chaotic fun for me. Though I suppose it's not fun after the fact.

thought for food

8:13 AM

It's interesting how much you can learn about a book from just browsing the index :P

user400188

@thoughtforfood I've thought that from time to time too; but usually upon closer inspection I haven't learned anything from it.

thought for food

It really depends how much effort the author has put into it, no? @user400188

Also the table of contents, of course.

user400188

@thoughtforfood I was under the impression that index was just the title and location of somehting in a publication. I guess if you added a description of the subject in the index it would teach you something.

thought for food

8:30 AM

Descriptive titles is what I was talking about @user400188

and descriptive phrases too

user228700

8:42 AM

Hello, everyone :-)

user228700

I have a quick question about the composition of functions. For two functions $f$ and $g$, which are inverse of each other, how is it that $f\circ g= g \circ f$?

Tobias Kildetoft

@Kaumudi.H By definition of being inverse both of those are the identity

user228700

$f \circ g$ gives $y$ where as $g \circ f$ gives $x$, no?

Balarka Sen

Domain and range of $f$ and $g$ are same in your case, yes?

Tobias Kildetoft

Ohh, I assumed that they were function from some set to itself

otherwise clearly they will never be equal

@BalarkaSen You want a hint on that puzzle btw?

user228700

8:46 AM

@BalarkaSen Dyou mean to ask "Domain of $f$ = Domain of $g$ etc., yes?" ?

Balarka Sen

I really gave up on it, but sure.

@Kaumudi Yeah. $f, g$ are supposed to be functions $A \to A$.

Tobias Kildetoft

@BalarkaSen Remember that the puzzle also has a name which might give a hint to what it is about

user228700

@BalarkaSen Right. OK, it makes sense, now. Thanks :-)

Balarka Sen

@TobiasKildetoft Had to google it. Sounds like a technical terminology in cinematography.

Tobias Kildetoft

8:59 AM

@BalarkaSen Ahh, I had not actually looked up the term, I just went with what it wounded like it should be about

Mike Miller

I haven't thought about it; rather I've been thinking about more mathematical puzzles

Tobias Kildetoft

Those are probably time better spent

user228700

I'm afraid I have a bit of a homework-tsy question.

user228700

I'm trying to find whether or not the functions $y=x^2+2x$ is onto.

user228700

The domain of this function is restricted such that it is bijective: $x \ge -1$

user228700

9:11 AM

Since there is a minima at $-1$, it is safe to conclude that this function is monotonically increasing from this point, because of which we know that this function is one-one.

user228700

Now for the onto part. So I've learned to do this by finding a function that gives me $x$ when I input $f(x)$ into it, such that $x \in$ Domain of $f$.

user228700

Usually I just do this by switching around the terms and manipulating the original function.

user228700

In this case, completing the square and all, I get $y= \pm \sqrt{x+1} -1$ as that function.

Balarka Sen

You just literally need to know when a solution to $x^2 + 2x = a$ exists, given an $a$ in whatever codomain you have.

user228700

...but you'll be quick to notice that that, in fact, is not a function because of the $\pm$.

user228700

9:14 AM

@BalarkaSen Hang on, let me really quickly finish.

user228700

But, OK, hear me out. My argument is that look, I manipulated the original function to get $x= \pm \sqrt{y+1} -1$

user228700

But the thing is, the minimum of the original function is $-1$, for which I get $x=-1$ and then for $0$, I get $0$ etc. I'm never going to use that $-$ case because including those will give me $x$s which aren't in the domain of the original function.

user228700

...by which I conclude that the negative sign shouldn't be there and that yes, I've found a function so yes, it's onto...aaand I'm starting to suspect that this whole line of reasoning is wrong so...is it?

user228700

Oh crap.

Balarka Sen

I don't even understand your line of reasoning. The point is simply that a solution to $x^2 + 2x - a = 0$ exists iff $(2)^2 + 4a \geq 0$, aka, $a \geq -1$. I don't know why you're trying to find an inverse function - onto functions don't always have inverses. This is a special case because it's bijective.

user228700

9:22 AM

For $0$ I get either $0$ or $-2$ and $-2$ isn't there in the domain of the function so wait, what am I supposed to do? Just ignore that negative sign?

Tobias Kildetoft

@BalarkaSen you need $\geq$

Balarka Sen

Fixed.

Transcript for

$Mathematics$ Mathematics