Nothing funny about it, @Ted, that's what's going to happen.

To say nothing of free booze... :)

AMAZING!! C# can handle $10000!$!!!!

@DonLarynx Takes forever though

Before I get dinner, @TedShifrin, could you check a quick calculation for me?

False alarm....

@DonLarynx Try instead to split the vector into equal subvectors :p

I can give it a shot, @MichaelA. Maybe.

OK @MikeMiller. On C with its standard metric, is \Delta |z|^2 = 4?

The Laplacian? Depends on whether you consider your laplacian to be $-f_{xx} - f_{yy}$ or positive. But I agree it's either 4 or -4.

i.e. it's going to depend on your sign conventions

I think most sign conventions in geometry books will give you the former one.

re-false alarm: YES IT CAN!!!!!! @N3

Cool. I meant d^*d + d^*d.

Right. Is your d^* = (-1)^{n(p+1)+1} * d *?

My head hurts, I'm going to get a beer

Join me @Ted

If so, you'll get a negative. (That's the sign convention Warner's book uses.)

I am now drinking a Corona. drinks corona

Double narration? @Don

@DanielFischer I have a quick question if you're still here. Doesn't the function $f(z) = \frac{1}{(e^{z}+z+1)^{2}+\pi^{2}}$ have poles at $z= - W_{k}(- \frac{1}{e}) -1 \pm i \pi$ where $W_{k}(z)$ is the $k$th branch of the Lambert W function? And aren't infinitely many of those points in the upper half-plane?

exception dead

@MikeMiller: I'll check my conventions. Thanks. I'll be back later.

Enjoy your dinner!

Bubye @MichaelA

I am trying to solve PE 495. This may or may not be stupid considering that I did not manage to solve PE 494.

PE 494 blew my confidence to shreds.

No, @blondblau. The antipodal map on $S^{2n}$ is not homotopic to the identity.

Not clear that's relevant @Mike

@TedShifrin If it didn't pass through the origin, you could divide out by the norm of that to get a homotopy between $f$ and the identity. But the anitpodal map is fixed point free and not homotopic to the identity.

No, there's $-x$, not $x$.

Fixed point free?

Boo.

Sorry, @blondblau, ignore me.

I missed a minus sign.

@blondblau: You were correct.

I agree with Ted, I was just busy being an embarassment.

Oh, hush, @Mike.

Because of the norm, $(1-t)f(x) - xt = 0$ can only happen if $t = 1/2$; i.e., $f(x)=x$. But $f$ has no fixed points.

@RandomVariable Unless I miscalculated, these are indeed poles. I don't know the Lambert $W$-function well enough to know where the poles are, but I'd be more than surprised if only finitely many of these poles were in the upper half-plane.

Evening @TedShifrin and @MikeMiller.

Hiya @DanielF

Nobody can see your emotes unless they're using an iDevice, @Ted.

According to my calculations, notepad's width is 1024 characters long.

Oh ugh ... :) @DanielF

listens to Orca by Deadmau5

No problem, @Ted, I can't decipher most smileys anyway.

Me neither :)

You done with your training, @DanielF?

@TedShifrin Not yet, still new to everything.

Has you know who quieted down?

No, who?

I suspect he means BD.

Bill

@TedShifrin paying the bills?

I suspect he would enjoy being called you-know-who in hushed tones.

Not yours, @N3B

Mine then, @Ted?

I'm not another old gay guy you're stealing money from, @Mike!

I only do that when I play poker, @Ted. I was hoping you'd just volunteer it :)

A beer makes my social personality come out.

Finish helping blondblau.

es tut mir Leid

@blondblau Suppose not. Then $$\frac{(1-t)f(x)+xt}{\|(1-t)f(x)+xt\|}$$ defines a homotopy between the identity and $f$. Not OK.

@DanielFischer I left a comment about that in response to an answer. But it has been seemingly ignored. So I just wanted to make sure I wasn't crazy.

@DonLarynx awesome song, I love the edm scene

@Jorge Great! College is full of it. What college are you going to?

one in Mexico

@RandomVariable You tend to be right about such things. You know quite a bit about them.

I leave it to you to translate, @blondblau.

@blondblau The fastest way to get over it is to find a new boyfriend.

@DanielFischer I wasn't offended. You didn't need to edit your post. Anyways, I have a paper about the branches of Lambert W function somewhere on my computer. When I first read it it, I found it very confusing. I should find it and see if it's any less confusing now.

@blondblau Why did he break up with you?

@blondblau I see. Well, all you need now is time. Time will heal these things.

$ 2$

@blondblau The people in this chat will tell you that I am always right, lol.

@blondblau Yes, you can also try that.

@blondblau I also broke up with my gf. Send me a pic and if you pass quals, you can go on a date with me

Yes @don and @blond can go on a date together. I will be the waiter.

@blondiebleau that's for me to know and for you to find out

Oh lord what's going on in here..

Bonne question @Kaj :) You get my message earlier?

@TedShifrin I thought you would be scolding everyone by now, lol.

Especially you, @Jasper

@TedShifrin, I did! I'm very pleased it's in that book. I think I have the .pdf saved somewhere on my computer. Looking forward to reading that section.

Cool :)

So many people in this chat have broken up, it seems.

Math is a demanding mistress/master, @Jasper

@TedShifrin Did I tell you that I never broke up with anyone because I never had anyone to break up with? LOL.

@JasperLoy my sentiments exactly.

Necessary but not sufficient ....

@blondblau I do. But I have now spent a large part of my life trying to recover from my mental illness, and is still trying. So I am not ready for a relationship.

hands @blondblau a Corona beer

@blondblau you sound like my ex, insecure of herself and frail

@blondblau you can get any man you want

@blondblau including me

offtopic

In all seriousness @Jasper you may recognize him @blondblau this video helped get my ex back (but i ended up dumping her) www.youtube.com/watch?v=2q5AWN81-3E

@DonLarynx Not again!

@Jasper judging by his thumbs up on his videos, that's not the correct statement

drinks two coronas at once

@blondblau No problem. Get better soon! :)

My mom told me I should stay in for new years eve.

I told my mum I would be at home on New Year's Eve.

@Jasper that's not right man

Anyway, I live with my mum, just us two.

@Jasper what city?

@DonLarynx I would prefer to keep my country a secret. It's not a good place to be in.

Oh yeah cause mentioning your country will make you look bad LOL

Nope, that's not the reason.

Iraq

I am who I am. The country has nothing to do with it. I don't mention it for some secret reasons.

OK @Jasper, because there are secret agents trying to hunt you.

@DonLarynx It is possible.

but very, very, very highly unlikely. You sound like John Nash in his prime, or lack thereof

Poor Nash, and poor me. I wonder what we did in our previous lives to deserve such kamma.

@Jasper nature vs nurture, choose one

@DonLarynx Well, as with all problems, it's always a bit of both.

For me it was 0.000001% nurture 99% nature.

Just go to sleep.

@blondblau how come?

@blondblau what is f?

If it was important, I don't think you would be posting it.

Oh, go on then

It is possible.

@Jasper: We need to go out on the 31st. There is no way we will stay in, despite our mothers.

@DonLarynx I need to stay at home and do something important. You have fun.

@Jasper please

You can't be this pathetic

@Jasper our ex-girlfriends will be kissing, in fact maybe even in bed with other males.

@Jasper you will be alone.

@Jasper ????

@blondblau My favourite country. I wish to be reborn there next life.

I REFUSE TO BE ALONE ON THE 31ST!!!

I WILL START OUT THE YEAR SOCIAL

FUCK YES

Thank you @blondblau

for giving me inspiration

@Jasper join me, and I will post pictures.

maybe not

but I will have fun and be social

and I encourage you too

@DonLarynx Send your pics to @blondblau. Then you can go on a date with her.

your mental problems will go away, but you must have faith

please @Jasper

@don By the way, did I tell you I am 33? I think you are probably 22.

@Jasper I am 20.

@Jasper what has 33 have to do with anything

you were meant to live

@DonLarynx Nothing. Just making small talk.

life is too short, oh too young

I am going to sleep now.

@Jasper you will be highly disapppointed

@PedroTamaroff A moderator should be a role model. In particular, they should be polite, e.g. they should not post comments calling other users "incosiderate" for choosing to teach as they prefer. Also, please keep in mind that folks don't necessarily see earlier answers if they started composing beforehand, paused, then comntinued (notification is not always reliable). Hopefully you will edit the comment to be more polite.

@Pedro I don't believe Bill, in that a mod should be a role model. They are there to dictate between what's wrong and right.

@BillDubuque, who died and appointed you judge and jury? I have had my teaching toes stepped on by plenty of you who saw fit to interrupt my conversations with OPs with complete solutions. Your viewpoint, albeit one of several, is far from universal. Stop being a bully.

:O

cyber-bully?

or troll...

$\Huge\scr T\Huge \color{green}{\cal h \frak e}\color{Red}{ original }skull pa troll\text{ & }\large\scr{cyberbully} Hunter ... . . .$

There's not even 4 users in this room AND there are 4 stars

No need to get rude here.

Haha did he get banned for that

Cusp point and straightness of a smooth curve.

@ElfSlice One of his messages got flagged by 6 users, causing an automatic 30-minute chat suspension

I know how the autoban system works

Trust me

Very interesting just how many users showed up in quick succession after I threw a flag.

@KajHansen Flags automatically notify all moderators and users with 10k rep or more.

wheee flags

I guess I learn something new every day :D I haven't paid much attention personally.

@Doorknob冰 I do have 10K rep here, but never saw a flag. Was this retired with 10K flag queue, by any chance?

@Behaviour It was handled... quite quickly.

(as in, a matter of seconds)

I'm not sure deleting the rest of his messages was really necessary.

Blatant personal attacks are by no means appropriate for the Stack Exchange network.

I can't even see who had a message removed.

Don

Oh, I see.

Nice hat @ElfSlice

My life significantly improved after realizing \setminus is a thing in LaTeX.

I used to exit math mode and just type a \

oh? I'm in the habit of typing \backslash

@KajHansen Why not use $A - B$?

Test: $\backslash$ $\setminus$

$A\setminus B$ vs. $A\backslash B$

@DanielFischer, I guess I could, but I've never been a big fan of that notation. I've always thought it looks bizarre, which is irrational I admit.

@DonLarynx Keep it calm please.

Yes Daniel.

Listen to him pal

@skull I'm not your pal, mate

ok np

blissfully ignorant of what is going on Back to learning about fundamental groups

Those are nice.

Looks like I made someone mad. I'm getting serial downvoted.

@Kaj Report them

I am trying to figure out bijective functions in C++ right now. This is very difficult.

@KajHansen An automated script will reverse them within 24 hours. (If it doesn't, then you can try contacting the SE team.)

Thanks, @Doorknob冰

I remember my first serial downvote. They eventually got reversed.

(I was the victim)

making SE gifs is fun

how u do dat @ElfSlice

@DonLarynx Adobe After Effects

Do all WB hats disappear eventually? After the 1st?

@DonLarynx After Jan 5, yes.

nvm

@DonLarynx just screencap your avatar wearing the hat and then use that as your new avatar. Win

@JMoravitz Like I did :)

....Thanks for downvoting all my stuff. Now that you have your hat, please reverse them.

@JM img1.wikia.nocookie.net/__cb20140924214801/familyguy/images/8/…

Besides, there are plenty of low-quality questions on main to downvote over the course of a day.

@KajHansen Don hasn't voted today. He's just trying to provoke you.

I'm so confused. Thanks @DanielFischer. I think I'll just wait for that script to kick in and take a break from the chat for a bit.

Later my friend.

Out of curiosity, to those of you in the room who teach, do you recommend MSE to your students? Or given the reputation it has of being abused as a free homework service, do you not tell them about it?

I show MSE to my friends and I don't really believe they look at it

Last semester, I recommended various links to videos by PatrickJMT and Kahn Academy if they wanted additional sources to study from, but I'm hesitant to offer them a link to here given the ease to get answers without learning

I'm still rather new to teaching (still only a Teaching Assistant), so trying to feel out what boundaries should be set

Remember: We require users to show an effort at answering the question or the question will be closed @JM

Help Help Help

HeLP!

Wow I absolutely hated PDE's. Good luck @FreeMind.

Nikon is set to join other camera manufacturers in taking advantage of the “selfie” craze, a new term for an old action of merely taking a photo of yourself – now with twice as much narcissistic vigor.

@FreeMind is your question simply about the choice of using dummy variables? Why we used $t$ instead of $x$ in line 5.12?

notice that it is a definite integral, and as such will equate to a scalar in the end. As a result, it didn't matter whether we used a $t$, a $\tau$, a $\heartsuit$ or whatever. Whichever symbol we use to integrate by, it will come out the same. In particular they chose to not use $x$ so that they could come up with an expression for $f(x)$ later on while using the work they did before.

@JM I'm considering recommending it next quarter to my linear algebra students, with the caveat that if I see them posting homework rather than ask for help they're in deep trouble.

Why tempt them?

Because MSE can be a valuable resource.

Certainly it has been for me.

True, but you may end up just sending all your time trying to enforce your "deep trouble"

In b4 "Why is the system 2x = 4 and 4x = 8 linearly independent?"

I guess the question comes down to the maturity of the students and whether you think they would abuse it or not. For graduate students, I would hope that they have enough integrity to avoid using it for graded assignments. I on the other hand have a class of jocks,

Jocks will abuse it for sure.

Hi :-)

:P

Yes, I might wait until I get upper division students. :)

Maturity is an important factor.

I think I will watch RuneScape videos for an hour and fall asleep.

They are very funny.

Have fun.

Thanks mate

Hi @MikeMiller.

Hi @MichaelA, I just got done losing at poker

@MikeMiller You should try winning next time. I've heard it's more fun.

Well, I tried that this time, but it didn't work out.

So we only had a moment, but I heard you're into complex geometry?

You heard correctly.

What're you looking at?

I'm going to try to solve as many project euler problems as i can tomorrow starting at 7am and ending at 5pm. Be prepared @Jorge @N3

Well, for my orals prep I am looking at Chapters 0, 1, and some of 2 of Griffiths & Harris. Also Milnor & Stasheff's Characteristic Classes. Aside from that, I am trying to read up about the Frolicher Spectral Sequence and differential graded algebras. How about yourself?

Could someone remind me the name of the theorem which states that the area of two triangles of equal base and equal height remains the same regardless where the vertices themselves are placed? Similarly, a stack of coins has the same volume whether slanted or straight

Any suggestions on "the best" book for topology?

Preferably a book that covered all areas of topology.

@JM: For your first theorem, wouldn't the perpendicular lines formed by the length of the base and height (which stays the same) be constant? So it doesn't move. Thus, $A=.5bh$. And this is called the third grade theorem, named after when you learned the formula.

@JM: The vertices can't move.

@JM: For your second, don't you notice that the individual coin stays constant? Thus, the sum of the volumes is the same.

@JM for many coins you can just perform an integral.

Of course, I understand the use of the theorem, but didn't know if it had a specific name, as it has been known since the greeks (or before)

I was hoping to have a fancy name to give it to use in the post math.stackexchange.com/questions/1084215/… here

Oops, sorry for the lack of response @MichaelAlbanese! I guess I'm turning into a topologist. I'm taking a class on gauge theory next quarter. Right now I'm reading about the hodge theorem and characteristic classes too (I don't really like Milnor's book; I usually find myself using it to figure out what topics to read about, and finding other places to read about them).

You can call it the JM theorem if it makes you feel special.

feels jaded after my ban

@GustavoMontano I guess Munkres or something is canonical, but I never read it. I doubt there's a book that gives every area of topology equally good airtime, since every branch is very broad and very different.

If you had more specific goals for what you want to read, I could probably provide better recommendations.

I see.

You might find Hatcher's notes useful. Also Ted sent me some lecture notes of his. Maybe he will send them to you too if you ask.

What areas of topology do you find most interesting?

Also, what's with the light bulb on your logo @MikeMiller. Have the elections finished? Who got chosen?

I think Hatcher's notes are great, but pretty basic. I need to find a source on the obstruction theoretic viewpoint (since I don't like Milnor's), and similarly for the Thom spectra story. A friend recommended Kirk and Davis's book.

@GustavoMontano I dunno, I like them all. I'd suggest reading Guillemin and Pollack's 'differential topology', since it's not terribly difficult and a lot of fun.

Pedro, Jyrki, Daniel won. I have a lightbulb because I earned it.

Hmmm, perhaps I should do some research. What are the different areas of topology?

I dunno. I guess broadly one might say there's differential topology, general topology (though I don't know how active this is as a field anymore), algebraic topology; maybe someone might want to call geometric topology different than these... they're all sort of broad and ill-defined. (Though if something's firmly, say, algebraic topology - you'll know)

Perhaps 'what are the areas of topology' is the wrong question. What's your background? Have you had a general topology course? Like one that covers compactness, connectedness, other basic properties...

Yes I have.

I have done real analysis.

Differential Topology definitely sounds fun. I did a course last semester.

Course on what?

So maybe your question, more accurately, is "I liked my ___ topology course. I want to learn more. What's next?"

@MichaelAlbanese So are you enjoying G&H? What's the Frohlicher SS?

"Differential Geometry and Topology". I really enjoyed it. But I want to learn more maths.

I just want to know "more".

Starting with most fun :p .

What'd it cover?

@MikeMiller Yes. The Frolicher spectral sequence connects the Dolbeault cohomology of a complex manifold with the de Rham cohomology. For Kahler manifolds, things work out nicely (Betti numbers are sums of Hodge numbers, etc.), but it can be complicated in general.

Problem 21 solved @N3 @Jorge. You can run but you can't hide.

Some basic topology stemming from differential geometry. So things like Eulers characteristic, work with representing surfaces in some algebraic form -> fundamental polygons

Nothing too much.

@MichaelAlbanese I suppose when one says the de Rham cohomology, it's meant as a real manifold?

@GustavoMontano Well, I think everyone should probably learn the stuff in G&H, if just for funsies. And you might want to learn some algebraic topology too. I don't know a good source other than Hatcher, but I'm told he's harsh on someone starting on it. (I started on Hatcher after having already taken a course that spent some time on the fundamental group.)

@MikeMiller Sure. Technically it is the complexified de Rham cohomology of the underlying smooth manifold.

Great! Thanks for your advice @MikeMiller.

OK, sure. Is it a multiplicative SS? Can you recover the algebra structure on the cohomology ring from it?

I have no idea, I'm still trying to understand it.

Ah. Well, cool.

Hi @MikeMiller

hello

Greetings