Oh @Rafflesiaarnoldii is here. I had some questions about one of your blog article but I can't even remember what it was about...

Goodnight all.

bye skull

gruber

userx

cya @mick

@Rafflesiaarnoldii I meant how does the system decide where to place the bounties when a user is deleted.

@UserX You could post in a comment there when reading it. I reply to comments. Except those that are about me downvoting on Math.SE; those comments are very short-lived.

@Rafflesiaarnoldii All I remember is that it was an article where you said 0 was in the middle of the real number line and I had an objection. Can't remember the content, I remember(maybe) the date;2006

@UserX Whether the user is deleted or not does not matter; the process I described applies whenever the user who started the bounty fails to award it.

@Rafflesiaarnoldii That's not my question. When a user is deleted, the community bot places his rep points as bounty to questions from what I understood. How are these questions chosen?

@UserX No, you misunderstood. The user posted those bounties on their own, prior to deleting the account. When the account was deleted, the ownership of bounties was transferred to the Community bot. If the user simply deleted account, no such bounties would appear.

Ah that explains stuff

I think I remembered the context of the article; Understanding topology(?)

Do you remember such an article dated back around 2006?

@DanielFischer I've been wondering why you have "explicit write access" to the Tavern on Meta... were you one of the founding fathers or something?

Oh nevermind, it was MJD's blog after all ;P

@Rafflesiaarnoldii I spent a lot of time there in 2012, when Pops and so on were regulars there. Not so much lately.

Ohh lucky me. I am trying to find papers about $G(n,p)$ when $p=1/n$. Can anyone direct me to such? I can only finds one discussing the situation after the critical phase, before it, or near the ends of it..

@Studentmath what does that notation mean?

The random graph on $n$ vertices, with probability $p$ that two vertices are neighbours

Binomial random graph

Ah ha. I'll see if I can find something.

Thanks @Alexander!

I found some really nice papers (by Israeli and Korean researchers!) detailing very finely the case around the end of the critical phase, but never inside, certainly not exactly at $p=1/n$ :/

Any wisdom on this question I have? math.stackexchange.com/questions/1022551/…

@Clarinetist i think you will have trouble finding a book that covers all of those things and won't be boring to you

most likely the best approach would be to get a book on combo/graph theory and another one on sets and logic (maybe Naive Set Theory by Halmos)

@AlexanderGruber - Thanks for the Halmos recommendation. Much appreciated. :) I currently have Epp... and will probably use it for now. I feel though, that Epp doesn't cover enough on algorithms. What would you recommend for books on combinatorics and graph theory?

"You, my friend, are about to witness the best card trick there is. Here, take this ordinary deck of cards, and draw a hand of five cards from it. Choose them deliberately or randomly, whichever you prefer--but do not show them to me! Show them instead to my lovely assistant, who will now give me four of them: the 7 of spades, then the Q of hearts, "

the 8 of clubs, the 3 of diamonds. There is one card left in your hand, known only to you and my assistant. And the hidden card, my friend, is the K of clubs"

How is that done?

Watching this is as good as eating food

Never mind. I found chocolate cookies.

@Clarinetist There are more serious graph theory books out there, but Chartrand's is a good bang for your buck, and should do you right for the purposes of the GRE at least

if you want to go beyond that and are willing to put in the time, diestel and diestel is the standard for advanced undergrad/beginning grad graphs

Hi @Alex

@AlexanderGruber - Thanks. Anything for combinatorics and algorithms?

i took a combinatorics and graph theory combination course that used brualdi... i didn't like it and can't recommend it in good faith, but it is the only one I know of that fills the gap between chartrand and diestel.

For algorithms, they probably only mean the stuff you'd run into in a basic number theory course or a basic graph theory course, like minimal spanning trees and stuff. Cormen and Leiserson is a really great book about algorithms, though, really a good thing to pick up even if it does go beyond what you will need for GRE

@TedShifrin Hi there. what's up?

Hi @alizter, lol.

Thanks again @AlexanderGruber. I've also never taken Number Theory. Considering Ireland's text. Is it overkill for this exam?

@Clarinetist I don't intend to study discrete math for the GRE at all, lol. Penner's Discrete Mathematics covers logic, set theory, number theory, combinatorics and graph theory, five in one.

@JasperLoy lol

@Clarinetist Yeah, definitely. I haven't read it but looking at the intro i see what level it's written at

@Clarinetist Yes, it is overkill. GRE is extremely basic.

@Clarinetist It is overkill by about ten levels, lol.

K, I think I'll go with Cormen and Leiserson, along with Penner. I was really disappointed by Epp.

when the GRE guys say "number theory" what they really mean is modular arithmetic. They want you to know fermat's little theorem, $\mathbb{Z}/{mn}\mathbb{Z}\cong \mathbb{Z}/{m}\mathbb{Z}\oplus \mathbb{Z}/{n}\mathbb{Z}$ when $n$ and $m$ are coprime, what you can take inverses of modulo $n$, etc.

Isn't that all abstract algebra?

@Clarinetist Yup

We can never cover all the topics in GRE, so I thought I would just cover a large portion of it.

I wish they would put out a list of suggested texts.

I'm spoiled from being an actuary. We're directed to specific texts for our exams.

They would not want to promote some books over others and risk the wrath of some.

True, lol.

All I said was Munkres is terrible and it incurred the wrath of a few in here, lol.

@JasperLoy Munkres is terrible

I kinda remember that. Which one do you prefer again? Lol.

for not learning topology.

you must be nuts @Jasper. :)

I had to explain that terrible can just mean I don't like it, but they said that was misusing the word, which I don't think it is.

[opinion] If you think math texts are terrible, you should see some of these actuarial textbooks.[/opinion]

@Clarinetist or physics.

@AlexanderGruber Munkres point set topology is too long winded. His algebraic topology does not cover many theorems. His differential topology is too thin. I hate all his topology books.

@Khallil whatchya got

@Khallil - yeah, put out a link.

@AlexanderGruber I found the Landau Course of Theoretical Physics books, ten volumes in all, seems very good.

@JasperLoy I thought his point set topology was really good but I wish I would have taken it two years earlier. By the time I got to it I was really sick of proving theorems about metric spaces

I used to work for an actuarial study materials company. I was really getting frustrated when they used "probability space" and "sample space" interchangeably for an ENTIRE probability study manual. [I'm not working there anymore :) ]

@JasperLoy I haven't read it

@AlexanderGruber Neither have I, I just browse through books, not read them, but still I think I can give an opinion, lol.

@Khallil Correct.

My question is does the identity element of $H$ (which is called $1$) have to also be the identity element of $G$?

@Khallil - Yes (if I recall correctly).

@Khallil OK there is actually a kind of complicated answer to that

If the group operation is the same then yes

@AlexanderGruber - I think that's a safe assumption to make if they're just learning about subgroups... but I'm not an algebraist by any means, so I might be wrong. :P

Yep, the group operations are always assumed to be the same as far as I know!

but if you are using a different multiplication, then not necessarily. MOST books (and people) consider it necessary for the operation to the same, but some don't

That makes sense. Thanks!

The book I learned from used $1_{G}$ to make it clear it was the identity element from $G$, if I remember correctly.

the only reason I bring the other way up is that I was once very very confused on the math GRE about something like this

@AlexanderGruber I have not seen one where they don't.

@Jasper, since you ignore the most important thing in any math text — the exercises, your opinions are worthless.

@JasperLoy Bourbaki doesn't

remembers a really awful Abstract Algebra parody textbook that used the F-word everywhere

@Ted Is there any sense in which this question makes sense?

@TedShifrin Ouch, lol.

@Clarinetist Really? Are you talking about Fraleigh? F for Fraleigh?

@JasperLoy , no, I mean the F-word as in English profanity. :P

Okay, so I'm probably going to get flamed for this. I'm not a fan of Stewart. What's a good textbook on multivariable calculus for the Math GRE?

No, @Mike. Only cup products of mod 2 classes.

@Clarinetist I thought Rogawski was fine

The only way it could make sense to me is if in the bits involving $c_1\wedge w_2$ they were talking about taking the chern class mod 2, and that the integral was notation for Poincaré dual.

OH- I do have a good one though: div grad curl

Not Poincaré dual ... Just evaluate on the mod-2 fundamental class. It's dumb.

Isn't that the same thing? :)

To me, Poincaré duality is about intermediate homology and cohomology.

Is there such a thing as cohomotopy?

@Clarinetist There isn't a separate version of multivariable calculus for GRE exam. To get book recommendations, try these posts.

Yes, @Jasper.

@Rafflesiaarnoldii - I know that; I'm just not very satisfied with Stewart's exposition of multivariable calculus.

@Ted I consider it to be about everything, including the stuff above $n$ and below $0$. But I'm silly.

Yup. You are.

@Clarinetist It will suffice for GRE.

K. I think I'll just stick with Stewart to save $$.

@Clarinetist: What is important is speed at doing standard calc, mult calc, series, linear alg, so you have time for the harder stuff.

I was lucky and found the newest edition of Stewart for ~$75 at a bookstore.

@TedShifrin yeah i will second that

@TedShifrin - Indeed. The last time I took it, I had no problem with the calculus, but I had problems with everything else.

I didn't give myself enough time to study and won't let that happen again.

@Clarinetist And the edition of Stewart makes no difference since you are not taking a course based on it... they are all the same inside.

even my star students are not scoring as high as we'd like.

the math GRE is really a terrible thing imo because it concentrates on speed at the complete expense of depth. that isn't what math is about.

@Clarinetist You can try getting international editions on abebooks.com.

The best skill I had on that test is speed at evaluating integrals and being able to approximate integrals well.

@AlexanderGruber Then again, maybe the schools don't consider GRE a large factor in deciding?

@Alex: It's a way for students not at the top 10 schools to show they have basic knowledge. No one claims it predicts success in research.

Only reason I'm considering taking it is because I come from a middle-of-nowhere university and feel like I have to compensate for that. I just asked for three letters of recommendation - hoping they all had good things to say about me.

the worst part for me was becoming interested in a problem and not wanting to do the educated guess -> move on thing

um, the -1 map is not so esoteric :)

deleted because it sounded pompous

@Ted That's why it haunted me for days!

Well, often you are, @Mike ... Like Jasper. :D

:(

Conway, Complex Analysis Vol. I for Math GRE - overkill or not?

@Clarinetist It's OK, but maybe only 1 question on complex analysis will come out, lol.

Overkill.

Alternative recommendations?

@Jasper: Seriously, have you even taken it yet?

For the purposes of the GRE alone you might look up Xauchy's integral theorem on Wikipedia and do a couple problems about it.

@TedShifrin No, but I have seen samples.

Let the people who've taken it give the advice.

heh, see, must be true.

some basic theorems about analytic functions will probably help too, the theory questions don't get too in depth. just surface stuff.

Differential equations - Schaum's outline fine? Do I need to know all of the real analysis behind it?

I learned the differential equations out of the GRE practice book by Princeton review

i don't remember too much diffyQ on there. Probably just linear first order and separation of variables.

I get the feeling you're planning to study full courses on the stuff covered when you just need to know how to do the problems that show up

Concentrate on nailing the stuff you know. They don't expect you to know everything, @Clarinetist.

I expect to have a score of about 50% of the total points (score coming in less than a week!) and definitely don't feel good about that...

@Ted It is worth covering some differential equations (in a minor way, like Princeton Review). There were 4-5 diffyq problems on my test.

sure, at the level of the intro sophomore course, maybe one more advanced.

right, I'm not suggesting much.

Yeah, hate to say it, but I didn't choose the right courses for the Math GRE. I switched from actuarial science to statistics and really, the only courses I took that were good preparation outside of the calculus sequence were two semesters each of analysis and algebra.

@Clarinetist honestly that probably puts you in good shape for more of the exam than you'd think

there will be a bit of probability.

There is a myriad of probability in actuarial science.

I just feel like I have a huge gap in discrete math, differential eqs., and geometry especially.

i know. I'm teaching prob and half my class are people trying to get the actuarial certificate.

geometry?

I will be sooooo happy when I get my first actuarial credential next year.

I don't recall there being any geometry on there.

Yeah, there were at least 3 questions on the last Math GRE on geometry, one of which had a term I had never seen before.

No projective or diff geometry that I know of ...

what kind of questions, @Clarinetist?

Without diving into too much detail, it's definitely at a high-school level for geometry.

Right ... Like you need for calculus problems.

like trig type geometry?

or basic probability

I've tutored calculus for 4 years and have never used this stuff. I'm talking about stuff that you would use if you were to teach a high school geometry class.

@Clarinetist so you mean like, law of cosines, complement of an angle

that kind of biz

Nope, even more obscure than that.

ech

Ah, angle bisector divides opposite side ...

see, this is what i'm talking about... the test is written by non-mathematicians so they have no idea what is important to know

Non-mathematicians, @Alex?

I was really ticked. Right after the exam, I looked it up on Wikipedia and thought... well, that definition is very vague. I just checked - the term is in my Schaum's Outline for Geometry. Definitely will finish going through this when I'm done.

*this when I take the Math GRE next time

What term?

@TedShifrin Yeah... I have a hard time believing that there are people with graduate math experience over at ETS writing this stuff

Not sure if I'm allowed to release that information...

@AlexanderG I have a hard time believing there aren't

@Clarinetist Legally? Probably not. But I have talked at length about the stuff in my exam. They're not going to sue you.

Sure, they have math degrees, @Alex. I don't want a finite group theorist writing it :)

Well, there was a question about what a locus between two points is. I had never heard of the term and thought of a bug ('locust').

locus of points is totally standard ...

Oh, that's something about parabolas. Ted probably thinks you should know what it is. I've got no idea, though. :)

@MikeMiller there was one question on there where it had an additive cyclic group and it asked you which of several subsets was a subgroup, none of the choices contained 0

ended up one of them was a multiplicative group

Other than that, I think what really got me on the exam was the amount of topology.

a locus is a zero set of a function to me

most of it is basic analysis, @Clarinetist

errors happen, @Alex, I think that's more sign that the people writing it don't spend much time on it than that they farm it out to undergrads

that's a variety, @anon :)

@TedShifrin - My analysis courses didn't cover topology. (Yes, I know I probably should've learned it by myself... but time, time...)

@TedShifrin I didn't say anything about algebraic :-)

you misread what I wrote

connected, compact, closed, open in metric spaces is analysis, @Clarinetist

right. Still though, i think it applies there too

@TedShifrin - Yep, all of those terms are unfamiliar to me. Closest I've come to metric spaces in a course was talking about complete metric spaces.

even running on 2% of my brain that would never get past the filter. It was not written by an expert. at most, a mathematician who works far away from algebra, and didn't remember it well

i cover all those in $\Bbb R^n$ in my freshman/sophomore multivariable course, but it's not typical curriculum.

@Alexander I consider it far more likely they contract a few PhDs and don't spend a lot of time on it.

@Ted It's typical in an analysis class from my experience

For many reasons, I wish I went to a better math school.

Yup, should be, @Mike, but lots of schools teach watered-down curricula.

@skullpatrol what happened while I was gone?

@robjohn! Thanks for your help last night.

I am not looking forward to reading Baby Rudin for the first time. Hopefully what I've learned so far will help me get through it, but it's hard to not feel like my undergraduate background was insufficient compared to many others' backgrounds.

@TedShifrin Glad I could help. I could do f[11], but f[12] sent my laptop into conniptions.

Rudin is beyond what you need, although any grad students needs to learn most of Rudin early on.

@robjohn: I quit at 5.

@TedShifrin - Surprises me to hear that. I heard Rudin was necessary for passing the exam, and that Royden is overkill. I've even heard of people using Royden to study for the Math GRE.

@TedShifrin It handles those nicely :-)

@Clarinetist probably couldn't hurt to do the first couple chapters of rudin, but you don't need the whole thing

*passing = doing well, that is.

@AlexanderGruber Blasphemer! >8(

:-)

in life, I think one needs most of Rudin

Lol.

I don't believe Arzela-Ascoli or equicontinuity appear. Uniform continuity, yes. Uniform convergence, probably.

@robjohn Hahaha. if you think that's bad, you wouldn't like much about what I have to say about rudin outside the context of GRE prep. :p

@TedShifrin those are in Rudin, unless Krantz went out of the book for that.

Sure they are. Just saying they are beyond GRE level.

don't remember uniform convergence on my test

@TedShifrin Oh... one the test. Sorry

@AlexanderGruber I never had Rudin, but I did have Krantz, though I've never read his books

One last textbook question, I promise! What's a good for a numerical analysis text? Also, is there really just a ton of formulas to memorize for this section of the test (if there even are such questions)?

huh? there's no numerical analysis on the GRE, if that's what you're asking about.

@robjohn Rudin has good problems, but he sucks the life out of analysis. (of course, this is coming from someone who hates analysis, so grains of salt must be taken)

Know Taylor's Theorem!

See ets.org/gre/subject/about/content/mathematics : from the 25% section - Other topics: general topology, geometry, complex variables, probability and statistics, and numerical analysis .

There's no numerical analysis beyond Taylor's theorem in any test I've ever seen, or anyone I've ever talked to about the test they took.

There's no stats, either, from that same experience, but sometimes a probability question.

@AlexanderGruber I will say that Rudin is a bit slick; that is, he has slick proofs that sometimes lack the motivation one might want.

Yeah, I had two or three probability questions on the exam I had.

@robjohn one problem i have is his lack of motivating examples in general

@AlexanderGruber But I think the material is organized well, and with a good teacher to provide some of the missing motivation, it was a good book.

@AlexanderGruber - alternative to Rudin?

@Clarinetist become a belligerent finitist

for GRE prep any intro analysis book suffices; say, ken ross's book

@AlexanderGruber Krantz was an excellent teacher, so I may have glossed over some of the missing pieces of Rudin.

know what compactness, connectedness, etc are

People like Abbott. I like Wade's book ok ...

I suppose 'etc' is unhelpful.

continuity

sequences and subsequences, lots of things about the cantor set

@AlexanderGruber haven't you been patriotic long enough? when will the emperor be sitting in front of a new backdrop?

@MikeMiller I do need to make a new one. this was supposed to be for the 4th of July.

I remember

It's disappointing I forgot about Halloween

So, a crapstorm has passed.

Hello @AlexanderGruber, @MikeMiller, @TedShifrin, and @anon.

Hello @robjohn

@PedroTamaroff Yo

@PedroTamaroff eh?

@robjohn I'm finally learning complex analysis Rob.

@robjohn Truly.

@PedroTamaroff cool!

@PedroTamaroff what happened? I was gone all day

Thank you all for your help! Appreciate it! :D

@robjohn Classic drama.

@robjohn Chris posted some question of his without using [text](link) so I said "You'll never learn to [altext](link); will you?". He said "Kid, I'm not playing with your games. Talk like that with your mom, pap, and the professors you want to." I said "U MAD?" She responded something with "GFY", and got banned.

@PedroTamaroff I guess she did not understand what you meant by [text](link)

The rest may have been some bad feelings between you two?

@AlexanderGruber You didn't go Trick or Treating?

For those of you who have gone to graduate school (I assume the majority of you), what do you wish you had done while you were still in school? [Prospective grad student here.]

@PedroTamaroff who banned her? Was that Manishearth?

@PedroTamaroff or was it just the flags?

@robjohn I think he's referring to the 30-minute suspension that occurs when your posts are flagged enough

@MikeMiller Ah, so just the flags.

@Clarinetist I should've drank more orange juice while I could.

@PedroTamaroff You can't drink orange juice?

Oh joy... 16 pages of errata for Dummit and Foote, 3rd ed.

@MikeMiller So it appears that he did put her on a suspension

Ah, I hadn't noticed that. Sorry for the misinformation.

@MikeMiller No, I appreciate the information. I hate being gone when shit bad stuff goes down.

Hi @Pedro.

@TedShifrin So, the proof of Riemann's mapping theorem seems pretty obtuse to me.

aye

@PedroTamaroff it can be any shape you want ;-)

Wait, maybe the word is "obstruse"?

I am confused now. Heh.

Googles

I think it's rather a cute.

Yes.

Obstruse.

abstruse?

Yes.

Abstruse.

@Pedro The way you used obtuse is correct and common, at least in the vernacular.

@PedroTamaroff I was just going to suggest that that is what you meant

Yes. But I still think normal families rule :)

@TedShifrin OK, sure.

@TedShifrin Are you saying my family is abnormal?

@Pedro Wait until you look at the uniformization theorem. Now that's abobtusetruse.

It's nice how one asks so little from holomorphic functions and they give so much, eh? =)

@MikeMiller Never bumped into it.

And there's differential geometry lurking. See Narasimhan's lovely (hard) book.

@PedroTamaroff They just need a derivative...

@TedShifrin Ah?

i would not dare impugn your famiky, not having met you yet, @robjohn.

@PedroTamaroff Riemann mapping is a special case.

@PedroTamaroff but actually a complex derivative is a pretty strict thing.

elliptic operators and all ...

@MikeMiller What does the thm say?

@PedroTamaroff Simply connected Riemann surfaces are conformally equivalent to one of the disc, plane, or sphere.

Amusingly re: how much you ask of holomorphic functions; if you try to take it one division ring higher and ask about quaternionic differentiability (in the obvious sense), then the only functions you get are the linear and constant ones.

@robjohn how do I undo a downvote to an answer? It says the vote is locked until the answer gets edited

@TheArtist You don't, unless they edit the answer.

@MikeMiller what if I call it an accident that i downvoted ? :p I just want to cancel the Downvote :/

@MikeMiller pl0x MAIK

Who cares about ugly quaternions.

Damn physicists.

I've never pondered quaternionic derivatives.

Topologists, @Pedro.

Not really an accident....but yea

@TheArtist You might ask him to edit it.

@MikeMiller Really?

Yes.

Milnor's construction of exotic 7-spheres is done using quaternions.

well, of course :)

That the 3-sphere is a Lie group is eternally useful...

@robjohn I went to a huge punk music festival.

@MikeMiller Cool.

@MikeMiller I have an exercise for you.

alex, there's something you should know

thefestfl.com

what should I know @mike?

@MikeMiller Mike cannot count to potato.

punk is dead.

Take a normal family in $\mathcal C(X,\Bbb C)$ for $X$ a second countable space. Then it is locally bounded.

punk has been dead for decades.

no @Pedro

@MikeMiller Come on. Suppose not.

@MikeMiller Nahhhh

I've thought about normal families enough for one lifetime.

it's just better live.

this is like the sixth sense where Bruce Willis finds out he's dead. of course you're going to deny it for a little while. but it's better to know the truth.

thinking @Mike has so far had a very short lifetime

@Ted This changes nothing

what would you consider alive punk?

post-punk has been dead for almost as long. we've all moved on

It sounds like you just don't like punk.

nah, I'm just kidding.

@TheArtist Sorry, I misread. You have to wait until it is edited.

@AlexanderGruber where was that?

@robjohn Here in Gainesville

@robjohn I downvoted it, it was an answer that had +1 to my question. I made it -1 so a net =0 ....but now I want to remove my downvote

This is a big punk hub because against me! is from here

they have a couple festivals every year

@AlexanderGruber Ah. Not that I know much about punk.

@robjohn Honestly I didn't before I moved here :p

@robjohn oh :/ so should I put a comment saying I downvoted your answer please edit it so that I can remove it ? :p would that work? :)

@TheArtist There is like a 5 minute window to change your vote, then you have to wait until it is edited to change.

but, move to italy, they're gonna feed you spaghetti.

@TheArtist If they want you to change your vote, they will :-)

@AlexanderGruber That I like :-)

@robjohn done :)

I'd like to be fed spaghetti as well

@robjohn Is it good to ask the asker to accept the answer ? :)

@TheArtist I consider it in bad taste to ask someone to upvote or accept your own answer, but not to ask them to upvote or accept someone else's

@robjohn Thanks :) I just changed a comment. I felt bad too, that's why I asked you

@TheArtist That's just my opinion. Some people don't seem to have a problem asking someone to accept their answer.

@robjohn I know. I have seen top users commenting that :) that's how I learnt it :p

Baire's Theorem says that if $X$ is a complete metric space and $$X=\bigcup_{k=1}^{\infty}A_k,$$ then there exists an $n$ s.t. $\stackrel{\circ}{\overline{A_n}}\neq\emptyset$. However, is it possible to have $\stackrel{\circ}{A_k}=\emptyset$ for all $k$ ?

I don't know waht the $\circ$ notation means. Could you clarify?

@MikeMiller It's the interior.

Nvm, $X:=\mathbb{R}$ and $A_1:=\mathbb{Q}$, $A_2:=\mathbb{R}\backslash\mathbb{Q}$ is an example (which, indeed, should be the first one checks ^^)