Mathematics - 2014-12-23 (page 5 of 10)

6:00 PM

On the other hand, I'll note that (one interpretation of) those courses seem to be at a wide difference of 'level'. I won't note anything about this note, I'll just note it.

Andrew Thompson

@MikeMiller "For an average student in their fourth semester" might be better, although still not good.

Balarka Sen

LEL at "I won't note anything about this note, I'll just note it."

Mike Miller

Depends on what you mean by an average student. The average over all math students I've encountered couldn't handle anything close to that.

Balarka Sen

I think measure theory and manifolds vastly differ from number theory.

Andrew Thompson

@Alexander I prefer algebrastuff, but its ok.

Balarka Sen

6:01 PM

So the course is not quite "homogeneous".

Mike Miller

Nor should a choice of study be homogeneous...

@AlexanderGruber he caught on!

Balarka Sen

I study homogeneously, @MikeM

Alexander Gruber

@MikeMiller Blame the illuminati :-X

Mike Miller

Case in point, @BalarkaSen

Andrew Thompson

@MikeMiller By average math student I mean willing to work 50+ hours a week and mostly gets A's or B's.

Maybe there's a difference in workethic between the countries.

Mike Miller

6:03 PM

That does not sound like the average math student. Anyway, I don't think I will be able to tell you whether or not you could handle it no matter how much detail you gave me - this is a question for somebody who knows you well.

(If you are talking about yourself.)

epimorphic

@AlexanderGruber In this case there is also a potential answer (without steps, just a numerical value) in the question. Should anything be done about that?

Mike Miller

If there were a wide array of courses I wanted to take, but was worried I would not be able to handle all of them, I would sign up for them and then drop one if I decided it added too much work for too little gain.

Alexander Gruber

@epimorphic There isn't really anything that can be done. If I delete that, then those who saw it before it was deleted will have an advantage in the contest

All I can do is prevent further answers from being posted

r9m

@AndrewThompson wow .. that's not average man ! Thats a good student !! :D

Balarka Sen

@TedShifrin

epimorphic

6:05 PM

I see.

Ted Shifrin

is someone scratching at the door?

Balarka Sen

scratches

Alexander Gruber

@AndrewThompson Honestly in my experience @AndrewThompson the "willing to work" part is contingent upon how much you hate what you're doing. I would never be able to take even 2 of those courses at once.

Balarka Sen

@TedShifrin you still have me on ignore?

Alexander Gruber

But give me 4 comparable difficulty courses in the disciplines I like and I'd be doin great

It really depends on you man

Ted Shifrin

6:06 PM

You're provisionally off ignore, @Balarka ...

Balarka Sen

OH MAN

Mike Miller

Maybe we should trade off, @Ted.

Balarka Sen

That was unexpected.

Jorge Fernández

@AlexanderGruber It hasn't worked yet.

Ted Shifrin

What are your four courses, @AndrewT?

Alexander Gruber

6:06 PM

@JorgeFernández what?

Balarka Sen

@MikeMiller maybe not if I successfully compute $\pi_1$ of hopf knot complement?

Mike Miller

7 mins ago, by Andrew Thompson

Complex functions, measure theory, manifolds and number theory. Is that a manageable courseload for someone in their fourth semester?

Jorge Fernández

@AlexanderGruber you know

Kristoffer Ryhl

I believe this question now has ben reworded to fit our rules math.stackexchange.com/questions/1079010/… but we need another reopen vote

Ted Shifrin

Fourth semester of graduate school or fourth semester of undergraduate?

Mike Miller

6:07 PM

I would have voted to close that in its curent state, @KristofferRyhl, and indeed I will if it's reopened.

Ted Shifrin

Now @Balarka is doing topology I have long since forgotten.

Alexander Gruber

@JorgeFernández Hahaha. Oh, yeah. What a shame.

Balarka Sen

I am doing algebraic topology @Ted

Mike Miller

No, he's doing topology you helped me on before I took my quals.

Balarka Sen

It's great stuff.

Ted Shifrin

6:08 PM

So I see, @Balarka ... The complement of the Hopf link I can do, because I see that very concretely in $\Bbb R^3$. Do you?

r9m

LOL :P that's a good one ! :D

Mike Miller

Especially since you know what a knot is now, @BalarkaSen.

Balarka Sen

@TedShifrin I have ideas.

If you're going to listen, I can explain my ideas.

Ted Shifrin

@Mike: I remember very little these days. Barely my name. The retirement letter is written.

Mike Miller

@Ted Unrelatedly, I was at a gay italian birthday party the other night. It was fabulous.

Balarka Sen

6:09 PM

Alzheimer, @Ted.

Ted Shifrin

Nice, @Mike. Invite me next year :P

Mike Miller

Maybe you should move to Palm Springs instead of San Diego... if you can handle the heat.

(Some like it hot, you know.)

Ted Shifrin

Ugh, NO.

Mike Miller

That's where I am right now :)

Winter is a great time to be here.

Balarka Sen

@TedShifrin here are my ideas

Ted Shifrin

6:11 PM

Have you read about the Wirtinger presentation for $\pi_1(S^3-K)$, @Balarka?

Balarka Sen

I dunno what a wirtinger presentation is

i am doing it from scratch.

Mike Miller

So you weren't listening when I told you about it?

Ted Shifrin

What is the $z$ plane, @Balarka?

Daniel Rust

evening

Ted Shifrin

heya @DanielRust

Mike Miller

6:13 PM

The one represented by the ideal $\langle z \rangle$, @Ted, of course

Balarka Sen

smacks @Mike

Ted Shifrin

Oh, most of us would call that the $xy$-plane.

Balarka Sen

@TedShifrin The $xy$ plane.

OK, jinx.

Hullo @DanielRust

Jorge Fernández

Did someone delete my comment in this question? math.stackexchange.com/questions/1078971/…?

Ted Shifrin

@Balarka: My suggestion is to pick the most convenient locations for the two "circles." In particular, let one of them go through the point at $\infty$, so you have just ... um ... the $z$-axis.

BTW, @Mike, was it a gay Italian's birthday, or an Italian party? :D

Balarka Sen

6:14 PM

did you see all of my approach?

Mike Miller

He's doing the complement in $\Bbb R^3$, which is a little more complicated.

Balarka Sen

this too?

Mike Miller

It was a gay Italian's birthday, taking the form of an Italian party, populated by gay Italians.

I think I counted once, and the ratios were 20.5:2.5.

Ted Shifrin

Very cool, @Mike :) I imagine your Italian improved.

Daniel Fischer

@r9m You spend too much effort on making them good questions, that makes you lose all the pity-upvotes.

Ted Shifrin

6:15 PM

Ratios?

Daniel Fischer

Hello @Ted.

Mike Miller

Yes, I learned how to say Grazzi.

Daniel Rust

@MikeMiller you can just use Van Kampen to show that $\pi_1(\mathbb{R}^3\setminus L)=\pi_1(S^3\setminus L)$

Ted Shifrin

Hi @DanielF

Balarka Sen

That's just a deformation retract, @DanielRust

Oh wait

$S^3$

Confus.

Ted Shifrin

6:16 PM

Easier @DanielRust @Balarka: Just let the point that compactifies $\Bbb R^3$ to form $S^3$ be a different point not in the link.

Mike Miller

Yes, @DanielRust

Daniel Rust

where you view $S^3$ as the one-point compactification of 3-space

Balarka Sen

ah

Mike Miller

I've done this problem enough times :P

Alexander Gruber

@DanielFischer Enjoying your last hour of freedom?

Balarka Sen

6:17 PM

makes sense @Ted

Mike Miller

But if he'd like to fully describe the topology of the one fella...

Daniel Rust

I answered this exact question a week ago

Ted Shifrin

@Alex: He did not like that when I asked that question last night.

Mike Miller

he'd better not just ignore that point

Daniel Rust

1

A: How do I prove this using van-Kampen theorem informally ? (2)

An informal calculation might go as follows. First, let's "push" one of the circles to infinity so that we're instead removing a copy of $S^1$ from $\mathbb{R}^3$ and a copy of $\mathbb{R}$ which 'goes through' the circle and goes off towards infinity along the $z$-coordinate. You should hopefull...

Alexander Gruber

6:17 PM

@TedShifrin Hahaha :)

Balarka Sen

actually i was thinking something like thickening up the "hooks" sticking up from the z-plane onto (R+)^3

Mike Miller

@DanielRust Ted showed me the way to write down the def'n retraction by consider $S^3$ as a subset of $\Bbb C^2$, where it's really quite easy to just write it down.

Daniel Fischer

@AlexanderGruber Who knows?

Ted Shifrin

Damn, @Balarka's forsaking his algebra and talking about hooks ...

@Mike, Ted did? He didn't show. He just told you to do it.

Mike Miller

You, at some point, said "consider $S^3 \subset \Bbb C^2$", which was the needed clue...

Balarka Sen

6:19 PM

@TedShifrin I tried comm. alg. after a month of alg topo, but I can't see any of them, so I threw Atiyah-McDonald onto dustbin...

Mike Miller

Maybe you said more, maybe you said less, but that was the key idea, I'd say.

Balarka Sen

You've been ignoring me for quite a few month @TedShifrin

Ted Shifrin

Atiyah-Macdonald does not belong in a dust bin, but give it until you're, say, 18.

Studentmath

He's got married since then

Mike Miller

Atiyah has done enough math for seventeen lifetimes...

Balarka Sen

6:20 PM

@TedShifrin but my prof wants to teach me algebraic geometry. eh.

Daniel Rust

I saw Atiyah speak last year

he's a good speaker

Balarka Sen

@Studentmath No way

I am not going to be captured.

Ted Shifrin

He's a fabulous speaker, @DanielRust. But, as was the case with Raoul Bott, every time I heard Atiyah speak, it was so effortlessly presented that I couldn't reconstruct any of it a day later.

Heya @Studentmath

Studentmath

Hey Prof. @Ted

Mike Miller

@Balarka Lest you be like me, you shouldn't decide what you're going to do for the rest of your life until it's turned out you're already doing it.

Alexander Gruber

6:21 PM

@BalarkaSen you and i are not so different after all

Balarka Sen

every algebraist are abstractly isomorphic to each other

Mike Miller

I think I changed twice, or thrice, or twice thrice.

skullpatrol

Hi @KhallilBenyattou ^_^

Ted Shifrin

I got several messages from one of my students who's not fond of me, @Studentmath: what was the final exam score? what was the average? what was the standard deviation? I also told the student his/her cumulative average. He/she then wanted to know what the C+/B- cutoff was. Turns out there was a 10-point gap between his/her grade and the lowest B. This person still didn't know when to add and when to multiply ... in counting.

@Mike gives, surprisingly, excellent advice. Just keep learning math until you're quite advanced ... then decide.

Balarka Sen

so i shouldn't not Atiyah till 18

Studentmath

6:23 PM

@Ted At least he is aware of standard deviation.

Ted Shifrin

@Balarka, totally NOT true. Herstein and Michael Artin are very far from isomorphic, to pick two well-known names.

Mike Miller

Do what you want, @Balarka. You're just a kid.

Ted Shifrin

The sigma was huge (around 20%), @Studentmath. A number of extremely high and extremely low scores.

Studentmath

Isn't it usually so, in tests?

Balarka Sen

@MikeMiller But I am going to stick to alg topo for a while.

Mike Miller

6:24 PM

@AlexanderGruber Can you deal with this however it's appropriate to be dealt with?

Balarka Sen

I should go slow on at least something

Ted Shifrin

Yes, but it seemed worse in this class. I mean, I had a score of 10% on the final. I should really not have counted it.

Yes, @Balarka, you should.

skullpatrol

10% :O

Mike Miller

One of the TAs texted me last night asking if I was still in town, @Ted. And the grades aren't submitted for the students yet. The impression I take from this is that he needs someone else to do his part of the job... I'm not happy.

Studentmath

@Ted woha. How did he get the 10%, I am curious

Ted Shifrin

6:25 PM

And if you're going to learn some algebraic geometry, let it be concrete stuff like algebraic curves, not schemes. That can wait until you're 19.

Jasper Loy

I always preferred analysis to algebra, but maybe I was just using the wrong books. So I ain't gonna decide which I prefer until I finish my 12 holy books.

Balarka Sen

@TedShifrin I am trying to formalize the connection between galois theory and covering spaces to get free enough to handwave more

@TedShifrin yes, sure.

i am not going for schemes

prof just said he wants me to absorb the first chapter of Hartshone

Ted Shifrin

Lots of partial credit points, @Studentmath. This is a guy who didn't want to be in the course and never had time to work on it.

Jasper Loy

@BalarkaSen There is a book called Elementary Algebraic Geometry by Hulek. Maybe you should take a look at it.

Balarka Sen

nah

skullpatrol

6:26 PM

@TedShifrin Did you count it?

Ted Shifrin

Read Fulton or another algebraic curves book, @Balarka. You don't need to worry about arbitrary varieties yet.

Balarka Sen

i'll stick to algebraic topologist. i might become a topologist instead, now that i think about it.

Studentmath

@Ted ah, well. I don't think I could ever be a good teacher because I wouldn't remember all the personal stories behind each student

Ted Shifrin

A beautiful book you should look at is Miles Reid's "An Undergraduate Course in Algebraic Geometry," or some title like that.

skullpatrol

Btw Hello Professor :)

Balarka Sen

6:27 PM

or a hyperbolic geometer, seeing how much i find Gromov hyperbolicity interesting.

Mike Miller

@BalarkaSen What'd I tell you?

Ted Shifrin

Well, @Studentmath, I got slammed by several students on this round of evaluations. Not surprised that a few hated me, and less than a third of the students bothered to fill them out. I think they've decided that since I'm retiring I don't care. Very frustrating.

Balarka Sen

@MikeMiller Yes, you did

Mike Miller

I remind you: at this stage of your life, you do not know what a topologist is. Just enjoy yourself.

Jasper Loy

@TedShifrin Maybe you should try to be nicer. =)

Ted Shifrin

6:28 PM

Well, @Balarka, if you're going to hyperbolic geometry, you have a lot of calculus/analysis/geometry to learn.

Mike Miller

I'm thinking we really should trade off, @Ted...

Ted Shifrin

LOL @Mike. You don't get to retire, sorry.

So @Mike, why isn't that TA bugging the professor instead of you?

Balarka Sen

@TedShifrin I mean gromov hyperbolicity and that stuff. that is much closer to algebra.

Jasper Loy

@MikeMiller Even at my stage of life, I do not know what will happen next week.

Balarka Sen

but i guess i should do rudin at some point

Studentmath

6:29 PM

@Ted Blech. Well, students are like children - usually ungrateful

Ted Shifrin

Gromov is a hell of a differential geometer, @Balarka. Sorry, that won't do.

Mike Miller

Hell if I know, @Ted. He didn't say more after we both told him we're out of town.

Ted Shifrin

Your generation in the US is way more children than earlier in my career, @studentmath.

Alexander Gruber

@BalarkaSen personally I'd recommend not Rudin for you

Balarka Sen

@AlexanderGruber <--- true algebraist

Ted Shifrin

6:30 PM

@Alex: He'll be ok with Rudin. First, he's already learned some point set. Second, he hates pictures :P

Mike Miller

I can't cope with y'all.

Balarka Sen

@TedShifrin I? Hate pictures? No way.

I love pictures.

Ted Shifrin

"y'all" = Southern-speak

Balarka Sen

I love alg topo.

Jasper Loy

@BalarkaSen I have Rudin's 3 textbooks. They have exactly 0 pictures altogether.

Studentmath

6:31 PM

@Ted I'd say it's turning the same here, though slower and much less in Math/science. People tend to be more grateful and hard-working when they go for such. But then again, I have seen the opposite too

Ted Shifrin

Oh, then Rudin is terrible, @Balarka, unless you draw all your own pictures. He has none ... none. Whereas I put dozens of pictures in my algebra text :D

Mike Miller

He should draw his own pictures.

That's the best way to use Rudin.

Jasper Loy

@TedShifrin I actually think it's OK not to have pictures in a textbook, because the students should draw their own, lol.

Alexander Gruber

The best way to use Rudin is kindling.

Balarka Sen

@TedShifrin I saw your algebra text.

It's great.

Ted Shifrin

6:32 PM

@Jasper: In the ideal world, I agree, but many students don't know what pictures to draw.

Alexander Gruber

But i have no other recommendation for an analysis text

Jasper Loy

@BalarkaSen Where did you see it? I can't find it anywhere.

Mike Miller

@alex coincidentally, this is how I intend to use... you!!

Ted Shifrin

For example, I draw pictures of modding out rings and groups by ideals/subgroups ... and in class I color-code.

Balarka Sen

@JasperLoy My prof has a copy :P

Alexander Gruber

6:33 PM

@MikeMiller Still better than reading Rudin

Studentmath

@Alexander would you recommend an analysis text, at all?

Ted Shifrin

Thank you, @Balarka, but I honestly didn't think it would fit your taste at all.

Balarka Sen

He wouldn't @Studentmath

Alexander Gruber

@Studentmath there is this kind of old one that I like but it is lower level than rudin

I don't have a good alternative at that level

Balarka Sen

@TedShifrin I used to do mathematics keeping eyes closed a few months ago, but now I don't. ;)

Alexander Gruber

6:34 PM

The best alternative at that level is to stop believing in infinite sets

Ted Shifrin

Apostol has an advanced calculus text, which is a real analysis text. That's the book over which @Pedro and I met. It's quite good. Also, Protter and Morrey is a decent book. So is Wade.

Balarka Sen

Can't possibly as my prof is a hyperbolic geometer.

Ted Shifrin

smacks @Alex for heresy

Studentmath

@Alexander No need for AC then

Balarka Sen

He draws everything.

Alexander Gruber

6:34 PM

@Studentmath Exactly.

Mike Miller

you people.

Balarka Sen

@AlexanderGruber I hate finite groups.

Ted Shifrin

@Mike, you and I should both retire from here.

Mike Miller

OK. Bye.

Ted Shifrin

OK, Mike's out. ...

skullpatrol

6:35 PM

Don't smack my friend >8(

Studentmath

He was quick at it

Alexander Gruber

@BalarkaSen Shh shh you don't know what you're saying

@Studentmath like a bandaid

Balarka Sen

You and your pee groups.

Ted Shifrin

OK, I'll leave you to the heresy.

Balarka Sen

Wait @Ted

We haven't talked for ages.

:P

Ted Shifrin

6:36 PM

You've talked plenty without me, @Balarka!

Alexander Gruber

@Ted, do you have any good recommendation for integration-level analysis?

Balarka Sen

Nah.

I just talked with Mike

Alexander Gruber

Lebesgue and all of that

Studentmath

Mostly about him convincing you to uignore @Balarka @Ted

Alexander Gruber

"Measure theory" i believe they call it in faraway lands

Balarka Sen

6:36 PM

Shhh @Studentmath

Ted Shifrin

That's not my pedagogical expertise, @Alex. I grew up on Royden, but I'm more fond of integration than of measure theory, so I don't like it that much. Have you looked at Folland?

LOL @Studentmath ...

Balarka Sen

I hope to do Hatcher after Munkres.

Ted Shifrin

@Balarka will find that I'm not worth all the trouble.

Balarka Sen

I am doing algebraic topology very thoroughly.

Alexander Gruber

@TedShifrin No, I haven't really looked at anything. I have chosen to do analysis deeply out of order, like all other subjects I have taken

Ted Shifrin

6:38 PM

Hatcher has supremely hard and interesting exercises, @Balarka. By orders of magnitude better in that regard than any other topology text.

Balarka Sen

@TedShifrin I can't possibly not care for your opinion.

Alexander Gruber

next semester is introductory measure theory and lebesgue integrals; this semester was rigorous probability

Mike Miller

@Ted In the week when I ignored him, he just picked new targets. So surely this would just happen again if they ignored him too... :)

Studentmath

@Mike they all started talking analysis the moment you left

Mike Miller

Great!

Ted Shifrin

6:38 PM

I thought you'd left, @Mike.

Mike Miller

I saw that you didn't, @Ted, and I felt betrayed.

Ted Shifrin

Yup, @Alex, totally out of order.

Balarka Sen

LEL

@TedShifrin I look at Hatcher now and then.

It's a good book.

Ted Shifrin

There are beautifully powerful theorems in integration theory (like monotone and dominated convergence, both of which are used all over probability).

Balarka Sen

@Mike wants me to do Hatcher.

Ted Shifrin

6:39 PM

LOL @Mike

@Alex: You might prefer Royden, as he structures everything very systematically from measures. But take a look at Folland. What book is your course using?

Alexander Gruber

@TedShifrin Yeah, I proved those last semester. (in probability)

@TedShifrin We just came to the end of baby Rudin, I'm not sure what he's got planned for next semester.

Ted Shifrin

Baby Rudin for a grad course? Weird.

THe measure theory and multivariable analysis in there are both terrible.

Mike Miller

I'm glad you encouraged me to read Lawson's book, @Ted. Even though it's put me behind on everything else I need to read... :)

Ted Shifrin

Well, that's life, @Mike. Lawson is a master.

Alexander Gruber

@TedShifrin Yeah, I don't know, they make it mandatory for some reason. I think I would do better just self-studying and taking an exam.

Mike Miller

6:41 PM

At some point I need to quit and go learn the Hodge theorem.

Balarka Sen

@TedShifrin I've a categorical language for unifying galois theory of fields and covering spaces that I told to @Mike.

Ted Shifrin

I loved all the stuff he and Harvey did on currents in complex geometry.

Leave me out of that, @Balarka.

Mike Miller

And then I need to quit and go learn Thom spectra, and then I need to quit and go learn the theory of connections...

Shut up, @Balarka

Balarka Sen

I want to use it for handwaving.

The more you can handwave, the more you understand.

Mike Miller

OK, I really am swapping spots with you, @Ted.

Ted Shifrin

6:42 PM

As I was explaining yesterday, you understand connections in the abstract setting better after understanding what they're doing for surfaces in $\Bbb R^3$ ... I'm not a fan of top-down math learning.

Balarka Sen

@MikeMiller Well I formally write-down proofs too.

Mike Miller

There is a sense in which I don't care about surfaces in $\Bbb R^3$, as hypocritical as that makes me.

But yes... I understand.

Ted Shifrin

Otherwise you'll be a symbol-pusher like @Balarka, @Mike.

Daniel Fischer

Well, it looks like I picked up 20 rep in that weird time when this question moved meta -> main -> meta. — TRiG 1 hour ago

@MikeMiller ^^

Mike Miller

Saw it, @DanielF. I've got nothin' to do with it.

Daniel Fischer

6:44 PM

Move along, move along ...

Balarka Sen

I am not symbol pusher @Ted. You can't compare this Balarka with 6 months younger Balarka.

Ted Shifrin

I didn't follow that, @DanielF.

Mike Miller

Move along, please, @Ted

Ted Shifrin

LOL ...

Daniel Fischer

@TedShifrin Mike participated in an experiment.

Ted Shifrin

6:45 PM

Unwittingly? @DanielF

Daniel Fischer

No, wittingly.

Ted Shifrin

More like half-wittingly, then.

I bet Alec will come in and chew me out for insulting young'uns again.

Balarka Sen

You have me on ignore for ages, @Ted, and now you're imposing on the improved-me the prat-me habits.

Ted Shifrin

OK, @Balarka: I shall watch and see :D

Studentmath

I've been looking for a good question to answer on the main, couldn't find anything in probability or coding theory :/

Mike Miller

6:48 PM

It's a wasteland out there, @Studentmath

Balarka Sen

I hope to study dessins at some point.

Ted Shifrin

Yesterday I found a charming diff geo question from an algebraic geometry type faculty member at U Michigan.

Alexander Gruber

@Studentmath Ask one

Studentmath

@Mike they all get like 40 answers in a second or get closed immediately, the others are above my level usually

Chris's sis

@Venus did you make some progress on my problem?

Mike Miller

6:49 PM

David Speyer's question, @Ted? I liked his question and your answer.

Balarka Sen

David Speyer is a great guy.

I've been trying to understand one of his answers in MO for years.

Studentmath

@Alexander I should think of one, yes.. I mean, this one math.stackexchange.com/questions/1078743/… is nice, but already got all that's needed in the comments

Ted Shifrin

Speyer is a good guy.

Balarka Sen

Dis I am trying to understand.

Mike Miller

Yeah.