Mathematics - 2013-02-25 (page 1 of 5)

Jonas Teuwen

00:00

Is that by Schwartz (not Schwarz)?

Arkamis

Probably. I don't recall the proper spelling.

Kasper

@PeterTamaroff it works ! hahah brilliant

Peter Tamaroff

00:19

@Kasper Good.

@JonasTeuwen AH?

Jonas Teuwen

B?

Peter Tamaroff

@JonasTeuwen What are you referring to?

peoplepower

@PeterTamaroff Got a good headache?

Peter Tamaroff

@peoplepower When?

peoplepower

00:34

@PeterTamaroff Oops, do you have an algebra headache? (Jasper/Jason/Jacob asks about homework, I ask about headaches :))

Peter Tamaroff

@peoplepower Hahha, no, not today. I did get one the day before yesterday!

Now I got to the section on group acting on sets.

peoplepower

@PeterTamaroff Ah, not too bad.

Tim

Sorry to interrupt. A quick question: Can a metric induce a measure?

Can I ask you, @jonas?

Jonas Teuwen

No.

Tim

Do you mean a metric cannot induce a measure?

Jonas Teuwen

00:37

The answer is of course yes: the Lebesgue distance does.

No, you can't send me unsolicited requests just because I am in the room 8-(.

Euclidean distance that is.

Tim

Sorry, Jonas

Thanks, Jonas

Jonas Teuwen

But if you have a metric on the sets, you can do stuff like $d(A, B) = \mu(A \Delta B)$.

Tim

That is measure inducing metric on sets.

For a metric to induce a measure, it looks like the underlyng space must be an algebraic structure, such as a group?

Jonas Teuwen

00:55

Caratheodory.

Outer measure.

Joey Morani

Can anyone help me out with some simple algebra? If I have the equation 4t = 3k/7t - 5k would k = 11t/-2

Charlie

Hello @jonas how are you?

Jonas Teuwen

01:28

Hi.

Ok.

I think.

I need to sleep I think.

Jonas Teuwen

01:45

Good night guys!

Argon

Good night!

Peter Tamaroff

03:28

Does anyone know which book this is?

anon

rotman

Ethan

@JacobBlack

user19161

@Ethan Yes, my dear Ethan.

BenjaLim

@AlexYoucis Thanks for your comment on main. Is the functor $(-)^G$ an exact functor?

taking invariance an exact functor?

user19161

03:44

@ethan There is no need to remove that, and I have replied to your email.

Ethan

@JacobBlack So I can just keep the latex the way I wrote it down in that email?

user19161

@Ethan I did not check through, but it is the same as you would type something here.

Ethan

@JacobBlack It just looks like code, when I look at it

user19161

@Ethan Well, just compile it and see if it looks OK, I don't have TeX installed at the moment to test it.

Ethan

.. compile it?

user19161

03:52

@Ethan Don't you have TeXworks and TeX installed? If not just test it on the site but don't post, haha.

Ethan

@JacobBlack yes, but im not really good at using it, im tempted to just take a picture of it, and add that as an attachment

user19161

@Ethan Compile means transform the source code to the output.

user19161

@Ethan Well, if he replies he will use LaTeX as well, so get used to it. Don't forget me when you win the Fields medal, lol.

anon

@BenjaLim I don't think it is; Wikipedia says "The group cohomology functors H* in general measure the extent to which taking invariants doesn't respect exact sequences."

Ethan

@JacobBlack math.ucla.edu/~ntg, should I talk to Haruzo instead? I haven't sent it yet, also which of their emails do I use?

user19161

03:55

@Ethan Use the one you think they will most likely receive and read.

user19161

@Ethan Also, email the one most relevant to your interests. I think you can figure that out.

anon

@BenjaLim: Do you have some familiarity with diff geo? My understanding is that to check a map preserves area but is not a local isometry or conformal it suffices to check that their first fundamental forms are different but $\sqrt{EG-F^2}$ is the same for both. Just wanted to check my understanding is correct.

Ethan

04:08

@anon does $$\lim_{n\to\infty}\ln(n)\sum_{k=1}^n\frac{\mu(k)}{k}$$ exist?

anon

my answer hasn't changed since last time since I haven't pondered it :)

Peter Tamaroff

@Ethan Didn't Landau prove that $\sum \mu(k)/k=1$?

Ethan

what?

anon

no, it's 0, Peter

(reciprocal of zeta at s=1)

Ethan

do you mean $-\ln(k)$ in front?

Peter Tamaroff

04:12

@anon Oh, OK. It was something very similar then.

anon

right, probably what Ethan just mentioned

Peter Tamaroff

@anon That sounds like you're scolding me!

anon

:scold:

next time I will take off points!

Ethan

@anon is there a fast way I can convert somthing written in latex on here into like copy-able plain text

that can be read in an email

anon

depends what you want it to look like ... do you want something that converts latex code into plaintext equivalents?

Ethan

04:14

uh

anon

alpha has a teensy bit of functionality for that, but mostly I think it's up to you

Peter Tamaroff

In fact he (Landau) says he got his doctorate by studying what $$\sum_{n=1}^\infty \mu(n)/n$$ is.

Ethan

@anon how hard would it be to convert like 12 lines of latex on here to something I can read not as code. in an email

anon

@PeterTamaroff indeed - arxiv.org/PS_cache/arxiv/pdf/0803/0803.3787v2.pdf

Peter Tamaroff

@anon Sweet!

anon

04:16

@Ethan 5-10 minutes? if it's so much, you might as well copy the latex code into your email and attach its output as an image

Ethan

@anon how would I do that?

Sanchez

@anon, what you say about fundamental form is right

anon

@Ethan output a preview of it somewhere - for example in your latex document creator, math.se, codecogs, etc. and take a screenshot (I assume getting the picture is what you're concerned about)

Ethan

oh you mean like take a picture and use it as an attachment

anon

You can do screenshots in windows with Ctrl+PrntScrn (or Fn+Prt Sc, whatever, something like that). Then go into Paint and Ctrl+v to paste the image.

Ethan

04:20

ok

Peter Tamaroff

@Ethan JUst send the code and maybe anon can render it?

Ethan

ok

Peter Tamaroff

Or use MathType on a WinWORD file.

anon

pastebin it rather than posting long code in chat

Ethan

how do I pastebin it

nvm I am figuring it out

anon

04:22

go to pastebin.com, paste your code into the box, click submit, copy url, paste url here

Ethan

for paste exposure?

what do i do

anon

lol

Peter Tamaroff

@anon Have you ever read Landau's books?

anon

no

the options are yours to choose, Ethan. funny you would narrow in on that one instantly.

Ethan

pastebin.com/HaLQ0bwR

did that work?

I appreciate the help, thank you

@anon

Peter Tamaroff

04:25

@anon Have you read them?

anon

2 mins ago, by anon

no

Peter Tamaroff

@anon Odd. That is before my question.

Ethan

What kind of food do you like to eat peter

Peter Tamaroff

@Ethan Funny, I was just watching this

anon

@Ethan, you might as well just send it as a pdf, uploaded.net/file/h37f5zz6

Orange Harvester

04:29

@Ethan if you want to mail something, you can use pdf I guess. (I do not if there are people who hate attachments though.)

anon

@PeterTamaroff your question was "Have you ever read Landau's books?" right? In my window, it comes chronologically before my "no."

Peter Tamaroff

@anon Odd.

Orange Harvester

@PeterTamaroff I like eating zebra.

Peter Tamaroff

@Ethan I like pasta quite a lot. Also a good "rice+vegetables+chicken/meat" asian style thingy.

Ethan

@PeterTamaroff youtube.com/watch?v=gHCxdlZ7G18 ...

Peter Tamaroff

04:30

@Ethan Well, not plain pasta, no.

"I just posted this on a vegan facebook page"

Ethan

@PeterTamaroff do you watch tv

Peter Tamaroff

@Ethan Not really. Just when I get tired of thinking, which doesn't happen a lot.

Ethan

I hate sunday nights

Peter Tamaroff

@Ethan It is Monday here already =P!

Ethan

time?

Peter Tamaroff

04:37

1:40 aprox

Ethan

its 8:37 here

gota do my spanish work now, cause I don't do it during class..

Peter Tamaroff

@Ethan I can probably help. Hehehehe.

@Ethan Did ytou take that just now?

Ethan

no last friday on accident lol

Peter Tamaroff

@Ethan Accident?

anon

appreciate those big desks while they last

Ethan

04:45

I waste alot of paper

peoplepower

Write smaller.

Peter Tamaroff

@anon Hahaha, so true.

@Ethan If it's a personal vendentta to trees, I don't blame you.

Keep it up.

A Bear Grylls parody

I don't get tired of watching it.

Orange Harvester

@anon Eh, you don't have big desks in college?

Ethan

@PeterTamaroff

Peter Tamaroff

@Ethan Ah?

@OrangeHarvester Not me either.

anon

04:52

@OrangeHarvester nope, teensy tiny ones :(

Orange Harvester

:-(

anon

but my office has a desk and a couch and is right next to the bathrooms and the math lab I work at which also has a refrigerator, paper, printers etc. so I shouldn't complain

Alex Youcis

@Sanchez If you come on, I have a question for you.

Ethan

Peter Tamaroff

@anon You mean a math office or a "job" office?

Ethan

04:54

i took that now :p

anon

math

Peter Tamaroff

@Ethan Watch out, behind you!!!

Sanchez

@Alex, yes?

Peter Tamaroff

@anon Explain yerself!

Alex Youcis

@Sanchez OK THANK GOD. Do you..remember class field theory at all?

in particular the Galois cohomology stuff

Orange Harvester

04:55

@anon labs are always well furnished and stocked. Mine even had a microwave.

anon

oh yes, the microwave. our lab also stocks free drinks in its fridge :)

Sanchez

@Alex, not really, but go ahead

Peter Tamaroff

@anon What do you mean you have an office? You work at the uni?

Alex Youcis

@Sanchez Do you remember how we construct, for a local field K, the local Artin maps $$\phi_{L/K}$$ which map $$K^\times/Nm(L^\times)$$ isomorphically to to $$Gal(L/K)$$ where $$L/K$$ is a finite abelian extension?

anon

@PeterTamaroff due to my working closely with a couple profs, they converted one of the storage offices into being mine

Peter Tamaroff

04:59

@AlexYoucis Avoid double dollar signs unless utterly necessary!

@anon That sounds great!

Alex Youcis

@PeterTamaroff Does it make it centered and stuff? I don't actually see the rendering of the latex on my end of things.

Peter Tamaroff

@anon You're already working on some paper/thesis or working with them?

anon

I do p-adic number theory with one guy and diagrammatic algebra stuff with the either (hecke, temperley lieb, interested in going over braid actions and quantum sl2, etc).

@PeterTamaroff well, with the second guy I read papers

Sanchez

@Alex, not quite: I only remember what it should mean for unramified extensions

Can you remind me?

anon

and with the first guy I am slated to present something at a conference at the end of may

Peter Tamaroff

05:01

@anon so you're doing some investigation right? sounds advanced... like graduate level

Alex Youcis

@Sanchez Eh, it's kind of sketchy. It comes from the isomorphism $\widehat{H}^{-2}(Gal(L/K),\mathbb{Z})\to \widheat{H}^0(L/K)$ where $\widehat{H}$ is Tate cohomology. This is true because the pair (Gal(L/K),L^\times) satisfies Tate's theorem.

Sanchez

What is the sequence you are taking cohomology of?

anon

wat

Alex Youcis

@Sanchez You mean what sequence does Tate cohomology come from?

Sanchez

yes

Alex Youcis

05:05

Haha, yeah, that's not easy to answer. It comes from splicing together normal group homology and normal group cohomology--the negative indices are group homology and the positive indices are group cohomology, and $\widehat{H}^0(G,M)$ is $M^G/\text{Nm}(M)$.

Sanchez

is it $\mathcal{O}_L^{\times} \to L \to \mathbb{Z}$?

Alex Youcis

oh

Sanchez

Nope, I'm not asking where Tate cohomology comes from, I'm asking what short exact sequence you are taking the cohomology of.

Alex Youcis

We're not, well, not directly.

We get the isomorphism from Tate's theorem en.wikipedia.org/wiki/Tate_cohomology_group#Tate.27s_theorem

@anon What?

Sanchez

Hm okay. Then?

Alex Youcis

05:07

Then, what is my question? haha

Peter Tamaroff

@anon Do you understand this?

Alex Youcis

because actualy, you may be able to answer that without understanding anything I just said to you.

anon

@PeterTamaroff holy moley where did you get that? that is perfect!

Ethan

Peter always has a bunch of good articles

Sanchez

@Alex, hmm?

Alex Youcis

05:09

My question really boils down to a question between the profinite completion of K^\times and the "open profinite completion" of K^\times

Ethan

@PeterTamaroff do you still have the papers I asked for yesterday I lost them, and the pastepin expired

Alex Youcis

Ok, so using the above machinery we can take a direct limit and find that Gal(K^ab/K)

is isomorphioc to the inverse limit of K^\times/Nm(L^\times) as L ranges over the finite abelian extensions of K

But the existence theorem says that Nm(L^\times) as L/K ranges over the finite abelian extensions of K

is really just the set of open finite index subgroups of K^\times

Sanchez

Direct limit?

Alex Youcis

so Gal(K^ab/K) is the inverse limit of K^\times/N where N ranges over the open finite index subgroups

Sanchez

oh ok, go ahead

Alex Youcis

05:10

@Sanchez Hmm? What about direct limit?

Sanchez

You meant to say inverse limit in your first line I suppose, so I was a bit confused.

Do you mind putting dollar signs around the math expressions btw? It makes it easier to read.

Alex Youcis

Sure, sure.

Sanchez

Anyway, then?

Alex Youcis

Yes, I meant inverse limits.

So, my issue is that all of the above says, as I said, that Gal(K^ab/K) is isomorphic to the inverse limit of K^\times/N as N ranges over the open finite index subgroups of K^\times

But, it's often stated that Gal(K^ab/K) is isomorphic to the profinite completion of K^\times

Sanchez

Not quite, but then?

Alex Youcis

05:12

which is defined to be the inverse limit of K^\times/N as N ranges over just the finite index subgroups--no openeness condition

@Sanchez Not quite what?

Sanchez

$Gal(K^{ab}/K)$ is not isomorphic to the profinite completion of $K^{\times}$

Alex Youcis

not K^\times the profinite completion of K^\times

or that is what is often said

Sanchez

isomorphism isn't preserved under inverse limit, or am i wrong?

Orange Harvester

holy smoke is firefox's new pdf viewer the best thing since sliced bread or what?

Alex Youcis

@Sanchez It does if you have compatible isomorphisms for every element of the inverse system, as in our case

Peter Tamaroff

05:19

@anon so you do understand it?

@Ethan GRRRRR

Let me look!

Sanchez

@Alex, makes sense. Then?

anon

@PeterTamaroff the first couple pages

Peter Tamaroff

@anon What does "quantum" stand for?

BenjaLim

@anon No I'm sorry I'm just taking differential geometry this semester.

@Sanchez Hi!

@AlexYoucis Why is the functor $(-)^G$ exact?

Sanchez

@BenjaLim, hi.

BenjaLim

05:22

@Sanchez Man I spent like 2 hours yesterday in the library trying to do this problem in FUlton

@Sanchez and then the penultimate question came to me:

@Sanchez Why can we represent a point in $\Bbb{R}^2$ as the zero locus of a polynomial?

@Sanchez Then I was like

Of course we can !!!

just take $(x-a)^2 + (y-b)^2$ !!!!

Sanchez

Haha

anon

@PeterTamaroff it's not entirely well-defined. a "quantum deformation" of a space is a sort of noncommutative preimage of it that attaches extra information to its elements. for instance, the braid group (algebra) is such a deformation of the symmetric group (algebra).

Ethan

@PeterTamaroff thanks, I just need the last one you sent me

BenjaLim

@Sanchez Man after I got that one I was like boom motherfucker

Sanchez

lol

anon

05:24

If you look at braid diagrams and turn every crossing-over into simply a crossing (where we no longer know which string went over/under which), and interpret the resulting diagram as a way of permuting objects, we obtain a group homomorphism $B_n\to S_n$ (the kernel of which is the "pure" braid group)

Alex Youcis

@BenjaLim It's not. But, it's additive and additive functors take split sequences to exact split sequences

BenjaLim

@AlexYoucis Ok. Because I thought from your comment that it was exact.

Peter Tamaroff

@anon So the answer is 7.

BenjaLim

@AlexYoucis I think my answer is ok.

Alex Youcis

@BenjaLim It's actually naturally equivalent to a Hom functor

BenjaLim

05:25

naturally equivalent?

Peter Tamaroff

@BenjaLim It has no preservatives or colorants.

Alex Youcis

@BenjaLim The functors are "isomorphic"

Sanchez

@AlexYoucis, then?

BenjaLim

@AlexYoucis Ok.

Alex Youcis

@Sanchez Larry Washington fixed it lol, it's ok

anon

05:26

A^G is sorta like hom(K,A), considering K[G]-modules

Alex Youcis

@Sanchez Thanks though :)

Sanchez

oh lol. Just curious, what was your question supposed to be?

BenjaLim

@Sanchez math.stackexchange.com/questions/312899/…

@anon Sorta like?

anon

naturally isomorphic to, can be thought of, etc

Alex Youcis

@Sanchez You mean my question?

Sanchez

05:27

@AlexYoucis, yes.

BenjaLim

@anon Thanks for your comment on main to countinghaus' answer

anon

yes, it was my understanding of ch's answer

BenjaLim

@anon I think my answer is pretty low level compared to the other answers :D

Alex Youcis

@Sanchez It was basically the fact that an inverse limit over K^\times/N where N ranged over the open finite index subgroups was the same as the inverse limit over K^\times/N where N ranged over just the finite index subgroups

BenjaLim

@anon @AlexYoucis @Sanchez I need to go make some brownies now. Bye!

@Sanchez First meeting with my supervisor tomorrow on Fulton!!

anon

05:31

later

Peter Tamaroff

@BenjaLim Wait

Sanchez

@BenjaLim, good luck! :)

Peter Tamaroff

Who are the guys in your gravatar? @BenjaLim

BenjaLim

@PeterTamaroff yea?

@PeterTamaroff facebook.com/BelleandTheBonePeople?ref=ts&fref=ts

Alex Youcis

@BenjaLim SEe ya

Sanchez

05:33

@AlexYoucis, I'm a bit confused. I suppose you need some topology on your inverse limit so maybe you would at least require your finite index subgroups to be closed, which is equivalent to being open?

What did Washington say on this?

Alex Youcis

@Sanchez That was part of the issue. The profinite completion of a group needn't involve the group having a topology, my hairbrained idea of an "open profinite completion" did.

@Sanchez Regarding the inverse limit: Evey subgroup of finite index contains an open of finite index (this is what cofinal means).
This implies that the limits are the same. Think about the inverse limit in terms of compatible sequences. If xO=yO for some open subgroup, then xN=yN for
every subgroup N containing O. Therefore, if you have a sequence that is compatible for open subgroups, it is automatically compatible for all subgroups of finite index.

That was Larry

Sanchez

is it obvious that it's cofinal?

Alex Youcis

@Sanchez No, but it's not too hard to prove. It's in Milne for example.

Sanchez

Hm okay.

Alex Youcis

@Sanchez This was one of these examples where the answer wasn't "too hard" but because everyone just says "obviously by taking the limit..." you assume you have a misunderstanding--they are making it seem like it is obvious

Peter Tamaroff

05:36

@anon Man

I have a question I guess you can answer

Not an exercise.

Sanchez

@AlexYoucis, haha.

Alex Youcis

@Sanchez Damn number theorists

Sanchez

lol

Alex Youcis

@Sanchez Do you know Larry?

Sanchez

No.

Do you?

Peter Tamaroff

05:38

@anon I repeat: Not an exercise =)

anon

go on

Sanchez

Oh he's at Maryland! Somehow I always thought he's at Seattle Washington

Alex Youcis

@Sanchez Yeah haha. He's the instructor for my Class Field Theory course. He was also one of my letter writers for grad school--I talk to him all the time. He's like the coolest man I've ever met

Yeah, yeah!

Sanchez

That's awesome :)

Peter Tamaroff

Let $G$ be any group, and $S$ a subset of $G$.

Alex Youcis

05:39

@Sanchez Ever looked at any of his books?

Sanchez

Not really. Heard about his cyclotomic fields book though.

Did he do iwasawa theory in there?

Alex Youcis

@Sanchez Yes haha. He was a student of Iwasaw actually

Iwasawa*

Sanchez

Oooh that's awesome :)

skullpatrol

What makes him soo cool?

Peter Tamaroff

Then $\bigcup_{g\in G}gSg^{-1}$ generates the smallest normal subgroup containing $S$.

@anon

Alex Youcis

05:40

@skullpatrol Larry Washington?

Peter Tamaroff

On the other hand, if $S$ is a group $\bigcap_{g\in G}gSg^{-1}$ is the largest subgroup contained $H$.

@anon

skullpatrol

@AlexYoucis Yes.

Alex Youcis

@Sanchez Did you ever have a class with a writer of a famous book.

anon

Unions of subgroups need not be subgroups (not closed under multiplication), while intersections of subgroups always are.

Alex Youcis

@skullpatrol He's super smart, extremely personable, caring, and very funny. Just an overall awesome guy.

Peter Tamaroff

05:41

@anon Yes, yes.

Sanchez

@AlexYoucis, yes I suppose.

Peter Tamaroff

My question is

Alex Youcis

@Sanchez Were they what their book would suggest they were like? I'm always curious if you cna tell a professors personaltiy from their books.

2

skullpatrol

@AlexYoucis Good question :-)

Sanchez

@AlexYoucis, that I'm not so sure. The funny thing is, the people I like more/go to their lectures more don't write much; and for those who write more, somehow I didn't get to read their work.

Alex Youcis

05:44

@Sanchez Haha, that's fair enough.

@BenW. Have you had Eisenbud for a class?

Sanchez

Oh is BenW from Cal?

Peter Tamaroff

Could you shed some light on the idea of how $\bigcup$, $\bigcap$ and this "congujation" cosets relate to creating least and last normal subgroups. The thing is the following: I can prove they have the properties we seek, but I have to write them down. The author, on the other hand, talks about the action of $G$ on the coset space (...)

$G/H$ for $H\leq G$ and what it's kernel is, and gets to show it is $\cap ^g H$, and then says "We see easily that the RHS (this set) is the largest normal subgroup of $G$ contained in $H$.

@anon

I mean, we have $4$ properties here: It is a subgroup, it is normal, it is contained in $H$, and it is the largest wrt to inclusion.

How can we "easily see" that right away, by looking and how we're building it up?

OH, BTW, the action of $G$ on $G/H$ is $g(xH)=gxH$, @anon

Alex Youcis

@Sanchez I guess I perhaps should let him answer such questions.

Ben W.

@AlexYoucis I haven't. I have seen him walking around campus occasionally, but I think he's pretty busy with MSRI.

Sanchez

@AlexYoucis, sure.

Alex Youcis

05:47

@Sanchez Do you have opinions about Berkeley? I'm trying to make a decision between some schoools.

Ben W.

And yes to your question @Sanchez

anon

@PeterTamaroff If $N$ is normal in $G$ and a subgroup of $H$, then $N$ is contained in all of $H$'s conjugates (just conjugate the relation $N\le H$), hence in particular is contained in the intersection of all of $H$'s conjugates. Conversely the intersection is clearly a subgroup and it is normal, so it is the biggest.

Sanchez

@BenW. cool.

@AlexYoucis, I don't, and perhaps Ben W. is a better person to ask.

Alex Youcis

@BenW. How about Wodczicki...I probably butchered that.

Peter Tamaroff

@anon I know, that's what I did to conclude what the author claimed. So maybe there is not much more than that to it, is there?

Ben W.

05:48

@AlexYoucis I have opinions, anything in particular you're interested in?

Alex Youcis

@BenW. Everything man. Is there any reason you would not go there?

Ben W.

@AlexYoucis I took honors real analysis with Wodzicki in Fall 2010.

anon

@PeterTamaroff right, that is the way to "easily see" it

Peter Tamaroff

@anon Hmm, OK. Lazy author is lazy.

Alex Youcis

@BenW. Interesting man. Heard good things about him--he's an intense guy.

Peter Tamaroff

05:49

@BenW. What does "honors real analysis" mean?

anon

a real analysis class taken for honors credit

Peter Tamaroff

What does "honors credit" mean? =)

anon

proof you took a more advanced track

Ben W.

@AlexYoucis He's very intense. We didn't actually learn real analysis. We only did topology and about six weeks of studying partially ordered sets.

anon

six weeks, wow

Alex Youcis

05:51

@BenW. Haha, that's funny man. What book did you guys use?

Ben W.

I had to teach myself real analysis the winter break after, he didn't really stay on topic, but what he did teach was interesting I suppose.

@AlexYoucis We did one problem out of Rudin: Prove $\sqrt{12}$ is irrational. Then we used his personal notes for the rest of the semester.

Alex Youcis

@BenW. Haha, nice. You said you had Olsson, right? How was he?

Ben W.

I had a number theory class with Olsson the same semester. I can only say good things about him. He is very organized and clear, and very approachable.

Alex Youcis

@BenW. Good :) Also, "Dedekind-Macneille completion"

Really?

Peter Tamaroff

@anon $H$ is a group $\iff$ $gHg^{-1}$ is a group?

Alex Youcis

05:54

I've never even heard of that

Peter Tamaroff

I think so.

anon

@PeterTamaroff yes

Peter Tamaroff

@anon Gooooood.

Ben W.

@AlexYoucis I see you found his notes! I checked his site and the link isn't public anymore.

anon

automorphisms map subgroups to subgroups (in fact they induce endomorphisms on the lattice of subgroups)

Alex Youcis

05:56

@BenW. Haha, I did. I just...like...don't understand what the point of that is. I mean, it's interesting, but I feel like actual analysis is much more foundational.

Peter Tamaroff

@anon Ayesee.

Ben W.

@AlexYoucis I agree. For that reason I avoided taking honors complex analysis with him. My friend did, and learned manifold theory or something, but never actually learned complex analysis.

Peter Tamaroff

@anon I believe you might already be a professor when I get to my Algebra II course!

Alex Youcis

@BenW. Have you had Ogus?

Ben W.

@AlexYoucis Don't get me wrong, Wodzicki is a nice man, but his classes that year didn't teach what they were supposed to.

@AlexYoucis Never took a class with him. The joke around campus is that his name is an acronym of "A Short Guru."

Alex Youcis

06:00

Hahaha, I've heard similar things!

@BenW. So you said you had opinions. Care to share them? :)

Peter Tamaroff

Bye, peoples of the math.

Ben W.

@AlexYoucis I like the campus. The undergrads are nice and down to earth. The math program is strong, but I can't comment on graduate student life.

Alex Youcis

@BenW. Do I need a fixed-gear bicycle to be a cool guy?

Ben W.

The surrounding area is okay for a while, but the southside campus is urban and dingy. There are a lot of hipsters around campus. Lots ride fixies on upper sproul. :) I know you're probably joking, but bike theft is a problem on campus.

Alex Youcis

@BenW. Joke? Never! :) How crazy is the department size?

Ben W.

06:03

(Upper Sproul is the main entrance to campus.) I've never personally had a problem with crime, but we are close to Oakland, so there are daily robberies around the area.

Alex Youcis

@BenW. Maryland is pretty bad too :S

Ben W.

So at least you know how to hold your own! The department size is a boon I think, because there is probably an expert in nearly every branch of math.

Alex Youcis

@BenW. True. But I feel like it may be super competative because of it

Ben W.

@AlexYoucis Super competitive in what way? With other students, or for finding a good advisor?

Alex Youcis

@BenW. The latter

Orange Harvester

06:07

What kind of precautions do you guys have to take against robberies? (I have never been affected by robberies myself, though I have lived in a rough neighbourhood, hence I ask what gives.)

Ben W.

@AlexYoucis Maybe, I don't know what that's like personally. So I can't say.

@OrangeHarvester There is campus police. I haven't had a problem with crime even though I walk around campus at 2 am sometimes. Usually people who get robbed are doing something dumb, like working on a laptop outside at night.

When there are few people around.

Orange Harvester

@BenW. I see. So, people get robbed on campus? Who are the robbers? Are they from outside the university? If yes, how can they get inside the campus? Or are campus really porus?

Ben W.

@OrangeHarvester The robbers are usually just people unaffiliated with the campus. The university is public, and it's nested right in the middle of Berkeley. So you can walk right onto campus from the city street. There are no gates or barriers or anything.

Orange Harvester

@BenW. Ahaa. I see.

Ben W.

@OrangeHarvester If you're curious, the red brick is the edge of campus, and the intersection is the city. dailycal.org/2013/01/31/…

That's how close it is.

Orange Harvester

06:20

That's quiet close.

Ethan

06:50

$$198^2+10^2=34^3$$

Ethan

07:03

$$26^2+18^2=10^3$$

$$(2+6b-6b^2-2b^3)^2+(6b^2-2-2b^3+6b)^2=(2b^2+2)^3$$

$$2(a^2+ab+b^2)^2-(a+b)^4=a^4+b^4$$

$$abc,bac,bca,acb,cba$$

Eric

09:01

What does the cyclic group $\langle (2,2) \rangle $ represent?

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$Mathematics$ Mathematics