Mathematics - 2017-07-27 (page 4 of 4)

Ted Shifrin

23:00

Strang has good points (and I learned a lot about teaching linear algebra from him), but it's not a good book for a math major who wants to learn how to write careful mathematics.

Who are the authors of the other?

Faust7

despite me oddly preferring it over the first (guy skips alot of steps or uses only one example)

first ones authors are Daniel Norman and Dan wolczuk

Ted Shifrin

Strang and I are good friends, and I stole some ideas from him in writing my book.

OK, I don't know the other book.

Danu

I found the following in Besse's book (paragraph 9.53)

Ted Shifrin

Actually, one of the things I'm proudest of in my book, @Faust, no one ever teaches, and that's the computer graphics discussion in the last chapter.

Faust7

reading stranges book after taking a linear algerbra class it seems not bad

Ted Shifrin

23:01

I probably can't answer, @Danu, but go on.

Danu

Faust7

but if i was trying to learn from it i would be super lost

Danu

I need to use this last identity, but I don't really understand how to derive it.

Faust7

he only uses one example and solves it 3 diffrent ways alot of times

Lucas Henrique

@TedShifrin Is linear algebra related to it? :P

Faust7

23:02

More examples = more better!

Ted Shifrin

Oh, @Danu. That's the usual principal bundle definition of curvature (see Kobayashi-Nomizu, for example) if $M$ is the frame bundle over $B$.

Danu

Can you elaborate?

(precise reference to KN would also be great!)

Simply Beautiful Art

@TedShifrin numerical analysis?

Danu

What I remember is that if we have a connection one-form $A$ then the curvature is $F=dA+[A,A]$

Faust7

@TedShifrin Any chance you have old problems sets from undergraduate classes laying around?

Simply Beautiful Art

23:06

@Danu :O Since when were you a moderator?

Ted Shifrin

@Danu: That's mixing apples and oranges.

Danu

@TedShifrin Right.

So can you elaborate? :D

@SimplyBeautifulArt Years, literally.

I'm not a moderator on Mathematics.

Simply Beautiful Art

Oh lol

Danu

I'm a moderator on History of Science and Mathematics

Ted Shifrin

Look on p. 76-78 of KN, @Danu.

Simply Beautiful Art

23:07

@Danu That's cool

Danu

Vol 1 or 2, Ted?

Ted Shifrin

1

@Faust: Like for what classes?

Danu

In 1, I'm just seeing the structure equation as I just wrote it down explained

heather

hello, i have a question about a topology video i watched.

Ted Shifrin

The formula you asked about is on p. 78, @Danu.

Danu

23:09

Ah, do you mean corollary 5.3?

heather

it said that a donut and a coffee mug are topologically the same, but i don't get that for two reasons. first, it said to think of deforming the donut as if it was made of clay, without cutting or pasting, and by that logic, a donut and a sphere are topologically equivalent - just smoosh the donut in and reform.

Ted Shifrin

I put the book away already.

No, @heather, you can't get rid of the hole in the donut.

Lucas Henrique

I quit life

heather

@TedShifrin so clay is just a poor analogy?

the other thought is that the coffee mug has a hole for the handle, and a "hole" that is the emptiness in the middle of the coffee.

Daminark

@LucasHenrique Same tbh

Lucas Henrique

23:10

I was supposed to buy the abstract algebra book. The. Abstract. Algebra. Book.

Ted Shifrin

no, the place the coffee goes is outside of the surface, but the handle is the hole of the doughnut.

Daminark

Did you buy linear algebra? @Lucas

Ted Shifrin

I wondered, @Lucas. You probably shouldn't be wasting money on books, anyhow :P

Lucas Henrique

Yes.

@TedShifrin Welp, I want to be a mathematician so probably I'll waste a lot of money on books.

Ted Shifrin

Lucas, send me an email.

But my point was that if you were going to get linear algebra, you could have done that in Portuguese :P

Daminark

23:13

Once you're in college you'll have a library available so you won't have to worry too much about purchasing them

heather

which is more holes than a donut, but i guess you're not punching through the bottom of the mug, so it's technically only one hole...

Ted Shifrin

better to make things out of thing rubber than out of clay, @heather.

heather

but then how do you get from a donut to a coffee mug?

Faust7

@TedShifrin Anything interesting i have two 4 year gaps of no math in my short life and only having 4 months back at it this time around, well to be honest i have probally forgotten more than i ever learned.
the most heavy things i need to review still are linear algebra and multivariable calculus but id love some stuff on topology as well. the more problems i do the faster i seem to remember how everything works

Ted Shifrin

problem is that most of my homework sets refer to some textbook, @Faust, either my own or someone else's.

Faust7

23:15

ah fair enough =)

Ted Shifrin

@heather: grab on to the rubber donut by one "side" and push the other side around to make the coffee cup without the handle part.

@Faust: I can send you lots of exams, I suppose.

Faust7

perhaps you could recommend a good multivarable calculus textbook i refuse to open mine ever again anyway :p

heather

@TedShifrin i'm having trouble with what you mean, i'm sorry

Ted Shifrin

@Faust: For that I obviously prefer my own :P

Lucas Henrique

@TedShifrin yes, I bought it in Portuguese

Ted Shifrin

23:17

@heather: I don't know how to do this without pictures. Are you grabbing the rubber doughnut with your hand around the right part and your fingers going through the hole?

@Lucas: Well, that's good, at least. Email me re the other book.

heather

@TedShifrin yeah, grasping it like a suitcase handle.

Lucas Henrique

Doing this at this exact moment. Thank you so much, professor.

Akiva Weinberger

Ted Shifrin

Ah, DogAteMy to the rescue.

Akiva Weinberger

Gif:

Ted Shifrin

23:19

Thanks!

Akiva Weinberger

Ted Shifrin

Poifect.

heather

@AkivaWeinberger ah...lightbulb.

Ted Shifrin

resigns and gives the reigns to DogAteMy

Lucas Henrique

@Ted, I sent you an email.

Ted Shifrin

23:20

OK, @Lucas.

heather

i have another question, in the same vein - take a cylinder. that's topologically equivalent to a sphere, if i understand right. then stretch it, begin to curve it, until it is infinitesimally close to the starting point. that's still as I understand it equivalent to a sphere. if i then connect the two ends, that becomes a torus. why is that different?

Faust7

@TedShifrin seems my libary has it for some reason the used ones are alot more then the new ones on amazon O.o

Ted Shifrin

A cylinder with top and bottom? Like a can of soup.

Daminark

@TedShifrin Seems like a reigny day

Ted Shifrin

@Faust: Prices are absurd. I cannot justify them.

Akiva Weinberger

23:21

@heather Does your cylinder include the interior? In any case: Is the reverse transformation continuous?

Or would you have to cut it to reverse it?

Lucas Henrique

@AkivaWeinberger I always see this gif and I know it's related to math. Topology, differential "things" maybe?

Danu

I still don't quite understand what's going on @TedShifrin. Everything here is about curvature of principal bundles. I also don't quite understand what $R^\nabla$ is supposed to be in the picture I linked.

Akiva Weinberger

@LucasHenrique Topology. Showing that a donut is homeomorphic to a coffee cup.

heather

@Akiva, I'm picturing a solid can of soup, and yeah, you'd have to cut it to reverse it, once you fully connect it. but if you get it infinitesimally close, no, you wouldn't have to cut it.

Danu

I understand that the structure equation gives us $\mathcal V[X,Y]=-F(X,Y)$ for horizontal vectors on a principal bundle

Faust7

23:22

your not supposed to cut

Akiva Weinberger

@heather In addition, the transformation isn't bijective since the two circular faces of the can end up overlapping

Ted Shifrin

It's just the curvature 2-form as a Lie-algebra valued form, @Danu.

Danu

I'm pretty sure $R^\nabla$ is supposed to be the curvature on some vector bundle, not a principal one.

Akiva Weinberger

@heather What does "infinitesimally close" mean? If there's still space between the two circular faces, it's not a torus

heather

@Akiva, okay. i'm sorry, i'm not thinking about this quite as mathematically, just more playing around with it.

Ted Shifrin

23:23

Doesn't matter. You can do vector bundle or associated frame bundle. No difference.

You still get a $\mathfrak{gl}(k)$-valued form for curvature.

Faust7

@TedShifrin ill try the rental from the library and if i like it then ill drop the 200 bones on it.

Lucas Henrique

@AkivaWeinberger this kind of thing makes both happy, ("good") anxious, ("bad") anxious and scared of uni-lelel mathematics

heather

i just need to keep reading about it.

Meow Mix

hi

Ted Shifrin

@Faust, don't waste money ... :) Also, use the videos to help.

Daminark

23:25

@Meow hey hey hey look who it is!

Ted Shifrin

@Meow!

Danu

Also, what is $\pi_* $ doing there then? $R^\nabla$ does not seem to be a curvature form on the total space, but rather on the base @Ted.

Meow Mix

hi @TedShifrin @Daminark

how was europe ted

heather

@Meow! Haven't seen you in a while, how's a going?

Meow Mix

im ok most of the things ive been doing have to do with software

Ted Shifrin

23:25

@Danu: It doesn't matter. Curvature descends to the base anyhow.

Meow Mix

how about you?

Ted Shifrin

OK, I'm trying to do 5 things at once, and I cannot.

Danu

It matters to my level of understanding what's going on!

I'll lay off

heather

@MeowMix cool, what sorts of things?

Meow Mix

operating system development

Danu

23:26

I can ask a PhD student, since this is supposed to be easy I guess

Meow Mix

game disassembly

heather

wow

Meow Mix

and since its summer my sleep schedule is fucked :]

Daminark

Welcome to the club

Meow Mix

i wake up at 2, have breakfast and go back to sleep until about now when i get dinner and wake up

Faust7

23:27

@TedShifrin perhaps but a good book is a good book and i didn't waste those 8 years i wasnt in school =) but ill check out the video lectures.

Meow Mix

@heather how are your studies going?

Faust7

Anyway im going back to re-learning math you guys have a good day

heather

@MeowMix pretty good, reading tons about quantum computing, working on an experiment I hope to conduct. Dabbling a bit in optics and math as it comes up in my reading.

Meow Mix

haha i watched a video on quantum computing today

i was like "what the fuck" and got back to my silly classical computng nonsense

heather

=/

what video?

Meow Mix

23:30

im not sure, i think it was by IBM

heather

i found michael nielsen's videos pretty good

if you want, i have an introduction with some math written up (if you don't that's fine too)

Meow Mix

i swear if im going to have to write quantum assembly my brain is going to be fucked

feel free to drop that link, ill watch it when i get a chance

heather

michael nielsen videos: youtube.com/watch?v=X2q1PuI2RFI&list=PL1826E60FD05B44E4

my current draft (for the worldbuilding blog): medium.com/p/db86d1f1665a/edit

Meow Mix

alright thanks, putting into firefox pocket

heather

and if you want, there's a great little simulator, quirk, that you can mess around with.

Meow Mix

23:37

anyways just wanted to stop bye

hmm i definitely will, want to mess with it before the inevitable takeover of quantum computers

heather

well, not really an inevitable takeover

you're not going to use quantum computing to check your email; no efficiency gain

really, considering the currently discovered algorithms, it's going to have the biggest impacts on cryptography and communications

Meow Mix

i work with servers

so yes, my rsa shit is gonna be inevitably cracked and ill be sad :(

heather

maybe searching, though grover's algorithm doesn't have nearly as efficient gain as shor's algorithm

@MeowMix well, but there'll be new algorithms to protect things.

Meow Mix

i hope

dont want quantum strangers ssh'ing without permission

this seems interesting to mess with

im going to see what i can come up with

heather

i'd also check out qasm

quantum assembly

Meow Mix

23:41

thats a thing?????

everyone throw out your x86 computers, the future is now

heather

you may also wish to pop into the hbar and talk with Daniel Sank (a quantum computing researcher at Martinis Lab) and Bernardo Meurer (college student interested in quantum computing and computers)

Meow Mix

heh i dont think i have the smarts

heather

@MeowMix yup, if you use ibm quantum experience you can download your programs as qasm

Meow Mix

id probably fit more in some software oriented chat

heather

@MeowMix i knew nothing a couple months ago.

Akiva Weinberger

23:42

Hi what up

Long time no see Zach

Meow Mix

yeah

how have you been doing

Akiva Weinberger

Good

I'm in Argentina

learning Spanish

Meow Mix

really?

Akiva Weinberger

Puedo hacerme entendido más o menos

@MeowMix Yeah

Meow Mix

what's it like there?

Akiva Weinberger

23:46

Nice

Meow Mix

hows the weather below the equator?

Akiva Weinberger

Well it's winter here

Not south enough to snow

and it's been cold some days warm some others

Meow Mix

what you could do is

stay until december

when it becomes june again, go up north for summer

and when it becomes december, go down south again for more summer

and oscillate up and down

Akiva Weinberger

I mean I gotta go to school again in September

in NYC

Meow Mix

shh

i spent all my brain power thinking that up

Transcript for

$Mathematics$ Mathematics