Mathematics - 2015-02-27 (page 2 of 4)

(I kid - linear algebra is very beautiful, and many things that you hope might be true are true! You should cherish a linear algebra course dearly)

5:20 PM

Sounds like a nice class @yswong

Btw im currently in an ODE class right now

well, obviously it's $\Bbb Z^2 * \Bbb Z/2$, @Mike

Which requires Linear Algebra

@JulianRachman like whatever u had done the whole year is what comes in these exams....

Oh. Haha. Sorry

5:21 PM

the thing generated by $i_A$ and $i_B^{-1}$ is trivial.

Which i regretted not taking

What text, @yswong?

where did the $\Bbb Z/2$ come from?

@yswong You're going to take the 2nd semester of Linear Algebra without taking the 1st semester course?

@MikeMiller RP^2.

5:22 PM

@JulianRachman how much difficult is munkres

and how does that relate, @balarka?

I got exempted from the first one

I saw just the set theory and logic part so I want to know....@JulianRachman

But seriously based on the description given are those topics manageable?

what d'you mean, @Mike? take the cross cap and bits of the sphere and take the torus and bits of the sphere so that intersection def rets onto the circle.

5:24 PM

@Mike: What are your hypotheses? Isn't Schoenflies true in general with smoothness?

I guess I could keep harassing you or I could point out that van Kampen is a theorem about unions, not about connected sums

The group on the right is not $\Bbb Z_2$.

yikes.

we are computing fundamental group of the cross cap, not RP^2

But a connected sum is a union :P

LeGrandDODOM

@DanielFischer Tell me if I got your intentions right: considering circles with suitable radii $r_n$ and taking points evenly distributed on these circles

I'm not paying attention anymore, @Balarka.

5:25 PM

@yswong What textbook

Comment ça va, Dodo?

Oh, I see what you mean. Punctured $\Bbb{RP}^2$ is the Mobius strip.

@MikeMiller we are computing fundamental group of RP^2 minus a disk.

Yes. That's $\Bbb Z$.

yes, i know the cross cap is homeo to moebius strip

5:26 PM

hi mr @Pedro

:P

Then why do you think its fundamental group is $\Bbb Z_2$?

@MikeMiller I'm proctoring another exam today at UCLA.

sorry.

good timing, @robjohn ... He's sick again :D

5:26 PM

@robjohn ah... I won't be able to say hello, I'm home sick.

@MikeMiller because i messed up. i didn't write anything at all.

Wait a sec@Exterior don't u have the same avatar as Pedro's

that'll do it

@Mike, when you lived at Penn State in the real winter, did you get sick this much?

Don't remember.

That was like a year ago.

5:27 PM

so yeah, it's $\Bbb Z^2 * \Bbb Z$

Well my school dosent follow any particualr textbook

oh no, we have a Pedro lookalike.

Exterior

@SayanChattopadhyay haha looks like it

$\langle i_A, i_B^{-1} \rangle$ is trivial.

what

5:27 PM

lol @Exterior

shut up and calculate, @Balarka

the thing we quotient with.

If I refer to @Exterior, it shall be as ExteriorAlgebra.

i don't want to. boohoo. i want to handwave.

That gets you wrong answers.

5:28 PM

Well, often, so does calculation :D

@TedShifrin: Everything's smooth here. I know that if an $S^{n-1} \subset S^n$ bounds en embedded disc, it's isotopic to the standard embedding. I don't think it's a theorem that every embedded $S^{n-1}$ bounds an embedded disc.

Why is @MikeMiller so grumpy.....take it easy...

Hey user130018

Hi @yswong

(In particular, IIRC, smooth Schoenflies is open in dimension 4.)

5:29 PM

If u want to know i can show u the link to my school exam paper

Ok

bah. i could just actually do a cell decomposition.

darn you van kampen

Or you could finish what you started...

no. too much calculation.

i'll now handwave.

OK, back on ignore.

5:30 PM

clubs.ntu.edu.sg/spmsclub/math/PYP/…

nono.

@Balarka: I'm on Mike's side.

^

@yswong I think you can do it

ok, ok, i'll do both. happy?

but let me do it by cell decomposition first.

5:31 PM

Is that managable?

@teadawg: Haven't heard much from you lately.

A Beautiful Mind

I am not sleeping yet.

@Mike: I'm not at all an expert on this smooth/PL/top stuff.

@TedShifrin Professor u know any place to buy maths books online

we have a torus with a a hole deleted from the side. that's a $aba^{-1}b^{-1}c$. and an rp^2 with a hole deleted from the side. that's a $ababc$

5:32 PM

@TedShifrin: I'm trying to understand Ryan's calculation of the mapping class group of the torus. Provided (1), I understand the proof. If (1) generalizes to $n=3$, then the same calculation works on the 3-torus.

Which is what I really want.

@Sayan AbeBooks has some cheap ones

@Ted This work I'm doing with polylogs is taking up most of my free time :(
My time management skills are poor

Well, @teadawg, I guess it's good you're so fascinated by that stuff. :)

I wouldn't recommend buying from AbeBooks, very shady business IMO

weird. i get $\Bbb Z^4/<aba^{-1}b^{-1}cdcd>$. completely stupid.

5:35 PM

@Mike: I guess you already know all this.

@MikeMiller sorry to hear it. I hope you feel better. Today I wish I were home with a fire in my fireplace.

I don't know anything in particular about math books, no. I'm just trying to get rid of most of my 1000.

Right, @Ted: the ie at the end is what I mentioned above. For $S^2 \subset S^3$ it should be true, because small dimensions are good.

@robjohn Appreciate it. Is it cold out?

@Ted Do you still have that copy of Spivak?

@teadawg: I have a few third editions I'd be willing to part with. I have only one fourth edition, which I think I'll keep.

5:36 PM

@MikeMiller No, the marine layer is keeping the heat in.

@MikeMiller it's in the mid 60s

oh, I see: it's all about there being exotic $D^4$s. Maybe I can dig up a proof, since there aren't any exotic $D^3$s. Thanks, @Ted.

@Ted: before or after you move to CA?

@robjohn that's reasonable weather... I'd like to be enjoying it :P

I'll look forward to visiting you and your menagerie, @robjohn ... even though I haven't been invited :D

Before, @AlexWertheim. Woe is us!

@robjohn I've got tickets for a play tonight which I'm hoping I'll have recovered enough in time for...

5:38 PM

@TedShifrin as soon as you're settled in, I will send an engraved invitation ;-p

Yeah, @Alex, I have no desire to pack, transport tons of books I just barely ever use.

Engraved, huh? :D

@Mike: indeed! My book collection is desperately lacking.

@MikeMiller which one?

@robjohn Tokyo Rose's Last Tape

(btw, sorry to hear you're still not feeling well. Hope you feel better soon!)

5:39 PM

@TedShifrin I wish u could give me ur 1000 maths books

Well, today's day 3, which is when it cools off.

@Ted: makes the most sense. :(

@Ted when you moving to CA?

Not too easy to accomplish, @Sayan.

@Sayan it is difficult if you don't have a foundation

5:39 PM

@Ted Hmm, is there much of a difference between the 3rd and 4th editions? I'm aware that the 4th edition was published in 2008

Look at these looters trying to nab free books off @Ted

send me some of that, @Ted.

I'm going to sell esoteric stuff (like the complete works of Elie Cartan, Kodaira, etc.) to Zubal Books for epsilon.

perhaps some good book on algtop

@MikeMiller Sounds quite interesting. It's Friday evening. It is amazing how much better people feel on Friday evening. :-)

5:40 PM

:P

The 4th edition incorporated some of my changes to the text (especially on limits), @teadawg.

What kind of foundation

I hope to start going to redcat more as time goes on... seems like my kind of theater

Ted Shifirn:Here is my school exam paper: clubs.ntu.edu.sg/spmsclub/math/PYP/…

Not free, @user130018. But @Ted has good taste, and I'd be interested in buying them. However, I too have no desire to transport tons of books. So I was hoping it might be when we were in the same place.

5:40 PM

Do u think it is managable?

U mean calculus @JulianRachman

Anybody who wants to come collect books and transport them themselves is welcome to them ... but I'm already giving them away to colleagues and students.

Jeez, @AlexWertheim, I was hoping to get them for free. Don't make me look like a cheapskate here.

@MikeMiller I've never been there. We go to a lot of theater, but usually downtown.

Loools @Mike. :)

5:41 PM

@Alex: You have no idea I have good taste. Look at the people I know in here!

I live about 3 hours away, I could probably pay for shipping @Ted

@RandomVariable: Hey there!

@Sayan yes and more.

Hahaha, perhaps just books then, not people @Ted. ;)

How lucky @teadawg1337

5:42 PM

How wsa it Ted Shifrin

@Ted can I get some books????

was

Some time this summer, @Julian.

@Ted: What if me and Alex picked two books each, eh?

oh noes i think @Ted is ignoring me.. again.

:(

5:42 PM

More......like@JulianRachman

I need all the math I can get

Random Variable

@robjohn Hello.

Juilan which math level are u at now?

@Sayan set theory, and a little analysis

@Julian Analysis is beautiful stuff

5:43 PM

This move will cost me a fortune, even without packing and shipping hundreds of pounds of books ...

It is.

I need all the weapons of the 20 and 21st century so that I can tackle any question....@JulianRachman

@robjohn: Redcat is downtown. It's in the silly-looking Walt Disney theater.

Or rather, it is that theater.

Analysis both real and complex @JulianRachman

For munkres

Julian: Maybe u can try this set of notes. See what u can learn from here. saylor.org/site/wp-content/uploads/2011/12/…

5:45 PM

@yswong I am currently learning topology and beginning abstract algebra

Julian: These are algebra notes

OK I'll take a look at it

RIP Leonard Nimoy

Oh, I knew he'd been sick. Did he just die?

@Ted In that case, I'd feel guilty about having one of your copies of Spivak... Give 'em to colleagues and students, I can look for my own copy

5:46 PM

Yes, today

@Ted could I take a few books of your shoulders?

@teadawg: You don't need to be guilty. But I don't have the time (or the back) to ship lots of books to lots of people.

Are you going to still be teaching in CA

@Ted

No, @Julian. Not unless I really miss it and some place in San Diego wants to hire me as an adjunct to teach something decent.

I believe he said he was retiring from teaching after this semester IIRC

5:47 PM

But I'm not going to teach precalculus or beginning calculus for grad-student stipend.

@Ted leave some for me and when you come to CA I'll pick them up. I will

I might try to tutor some at-risk students ...

What's "at-risk" mean

Two days ago was national adjunct walk-out day. Apparently turnout was ~30 at the event we held about it here.

@Julian: I'm not moving stuff cross-country. It's very expensive to do so.

5:48 PM

Ted: whats pre- calculus. Never heard of it beforet

mr eyeglasses, I meant minority kids.

@yswong: In the US precalculus is the "college" course covering algebra and trigonometry and word problems to "prepare" students for calculus.

@Ted: you, Mike and I should write a paper called "Galois Representations of 4-Manifolds: A Complex-Geometric Approach" that will shake the foundations of the math world.

Honestly, my pre-calc course that I took in high school was 99% review

haha

LOL ... @Alex, the only thing I can contribute is the "... a geometric approach" subtitle that everyone pokes fun at me for :P

5:50 PM

i'd be love to see that paper

Ted: it works differently in my country. Do u want to know the curriculum structure of maths in my country.

@AlexWertheim My buddy Kevin likes toposes. We could include toposes.

presumably high school students actually learn math in your country, @ys

@Mike: Is that a word? Not topoi?

Blame Grothendieck, @Ted.

Ted: as in high school students.

Ted: nushigh.edu.sg/qql/slot/u186/…

5:51 PM

I would prefer topoi... but the other is standard.

I've never once heard it, @Mike ... until just now.

It's not your style of math.

actually, i think the group is ZZZ/<a^2b^2c^2=1>

Huh... apparently there's actually widespread disagreement.

@JulianRachman were u able to finish the second chapter of munkres

5:53 PM

OK, I guess I'll call them topoi. I didn't know I was allowed to.

Hehehe. Sounds good @Mike, I'll amend it. "Galois Representations of Topoi on 4-Manifolds: A Complex-Geometric Approach". I can see it now.

@Balarka: When you write $\Bbb Z^k$, you mean an abelian group? You should have free product?

Ask u all guys

Can i ask u all kinds

right, right. sorry.

dont ask to ask

5:54 PM

Just ask

Is there such a thing as finish learning mathmatics

derp.

hello sayan

@yswong: It's called dying.

Hi yash g

5:55 PM

@yswong There is always more to learn in the field of mathematics

Pedro Tamaroff

No. You'll know the most maths when you die.

Well, unless you die as @Ted points out...

That means u can never finish learning maths?

@SayanChattopadhyay , i don't use that name anymore

Not true, @Pedro. I probably know less now than I did 20 years ago.

5:56 PM

You can never finish learning anything

Even if u learn u would also not manage to learn everything?

This is getting rather philosophical....

There's too much.

i finished learning how to breathe years ago.( or did I?)

I mean even after u die u would also not be able to learn all of maths?

5:56 PM

Not really.

Knowledge is an ocean where u can go as deep as u want

OK now we're going into theology.

right, right so now let's try van kampen.

Lucky for me: Office hours (again) start in two minutes.

lol

5:58 PM

xD

$\pi_1(T \# \Bbb RP^2) \cong \pi_1(T-\{*\}) * \pi_1(\Bbb RP^2 - \{*\})/<\text{something}> \cong \Bbb Z * \Bbb Z * \Bbb Z/<\text{something}>$

well, that's not saying too much, @Balarka ...

Then where are u all at in the journey of mathematics already?