Hi @EYES @hippa

@BalarkaSen I am having trouble understanding this 'primitive root' thing.

:/

Anyone awake?

I'm here

Ah.

@JC574 Hi.

@Sawarnik hey :)

Barely, @Sawarnik

primitive roots of unity? primitive roots modulo n?

@JC574 modulo n

@teadawg1337 Morning or midnight?

@Sawarnik is there something in particular troubling you with them?

@Sawarnik Neither; afternoon slump, as evidenced by my atrocious spelling

@ᴇʏᴇs Are you here?

@JC574 not really, i have just started, but i find it different from the relative ease with which i went through phi and euler's theorem :D

@teadawg1337 i thought the spelling was intentional :D

My internet is all kinds of screwed up right now...

@JC574 you're familiar with De Rahm cohomology ?

@Sawarnik what about them?

I am familiar with The Ram.

@LeGrandDODOM I wouldn't say familiar. I did a project last summer on something related

@LeGrandDODOM! You're studying De Rham cohomology?

hee .. balarka replied to me after a long time..

@BalarkaSen no way :)

@BalarkaSen I am glad you are correcting Sayan's mistakes. I think he will take a very long time to master calculus.

well, why not? I am going to study that stuff.

@BalarkaSen cool!

Singular cohomology is particularly boring -- Ted says the real flavor comes from forms and stuff. It's a long way to go, though, seeing my background/

@ᴇʏᴇs I am very sad.

@BalarkaSen what have you studied? what's your background?

@BalarkaSen My algebra is way too lousy. Maybe in a year or two

i don't know much multivariable calculus for one to start on calculus on manifolds, @JC574

My stronghold is mostly algebra and topology.

@BalarkaSen Ah I'm in a similar position

You're thinking about studying that stuff too?

@LeGrandDODOM Grab Artin if you feel comfortable with geometry.

It's terse though, so watch out.

@BalarkaSen I'd like to study algebraic geometry, and I'm doing/going to do a related research project this summer too.

@JC574 Where do you study?

Cool beans. I dunno any algebraic geometry.

@JasperLoy What's with him?

I wouldn't use Artin as my main text for algebra, i find it's good for getting a general idea of things though

@Sawarnik Nothing.

@JC574 I like Dummit-Foote, but prefer Artin over it.

@JasperLoy :D

@BalarkaSen yeah was going to mention Dummit-Foote, my go-to

I guess @JC574 intends to keep it a secret from me.

@JasperLoy i dunno whether i want to say ;)

@JC574 You can just tell me it is a secret, instead of not replying.

@JasperLoy you're right, sorry

@JC574 For example, my location is a secret.

Dummit-Foote rambles on semidirect products way too much, neither taking Artin's style about not mentioning it at all nor introducing the cool general nonsense way of classifying groups (exact sequences, splitting lemma)

@JasperLoy I'd prefer to keep it a secret :)

@JC574 I just tell people I live in Antarctica these days.

@BalarkaSen that's a very fair criticism

@JasperLoy haha

@BalarkaSen Dummit and Foote is as dumb as a foot.

plus, their proof of fundamental theorem of galois theory is huge. when i read galois theory from it, it felt that they somehow want to avoid the inherited group structure on fields.

@JasperLoy damn it my foot.

I find Galois theory very hard.

@BalarkaSen There is art in Artin.

@JC574 What does your name mean?

@JasperLoy Some secret code.

@Sawarnik Why are you answering for him?

Hi @JasperLoy @Saw

I m guessing :D

@ᴇʏᴇs hey

@ᴇʏᴇs Bart, I think I only have 1 per cent chance of success, so I am very sad...

@Sawarnik You didn't tell me what your question on primitive roots was.

@BalarkaSen No question really, its just that I find it understanding a bit more difficult that the totient and other things you once tried to teach me :)

It's not really interesting if you don't know group theory, but the definition should be clear.

@BalarkaSen Btw, the definition here (en.wikipedia.org/wiki/Primitive_root_modulo_n ) than in my book, which states that a is primitive root if the order is phi(n)?

@ᴇʏᴇs Bart, do you have anything to say to me?

The thing is, $\Bbb Z_n$ is not a "group" for arbitrary integer $n$. There are many elements that are not invertible.

For example, $2 \bmod 6$ is not invertible in $\Bbb Z_6$

mr eyeglasses: Yes, finite dimensional spectral theorem, for sure.

Welcome back @Ted

So what we'd want is to have some "groupification" of this by collecting all the invertible elements mod n.

yes, @Balarka, nullity rank is basically the fundamental homomorphism theorem, right?

Here comes chef @ted.

yeah. boring. blah.

thanks, @teadawg ... done with office hours and back home ... waiting for the next major repair in the early morning.

@BalarkaSen i am not studying group theory yet :/

see, @Balarka, that's the trouble with going backwards ... many of the cool elementary results are just boring :P

@Sawarnik Now the problem with the set of all invertible elements mod n is that there is no good "presentation" known for it, i.e., we don't know what the generators are.

@TedShifrin One must try to go forwards in life. I must learn this lesson.

The generators of the group are precisely what we call primitive roots modulo n

I dunno, @Jasper .. I've often found myself going backwards to learn something I didn't know.

@TedShifrin You did?

@TedShifrin I mean not dwelling too much on the past.

Plenty, @Balarka. Ah, yes, @Jasper, particularly for you.

that makes me feel a bit better

@Balarka: My adviser once gave me the advice to try to prove theorems, and then go back and learn certain things when I needed to understand them to progress. I did a compromise :)

I think @BalarkaSen is Ramanujan incarnate.

no, I don't think that's right, @Jasper, but Chris'ssis thinks she is.

i guess the only thing in linear algebra i really need to know is billinear forms, i.e., inner products.

@JasperLoy i'd rather not.

@TedShifrin Rather, I think she is too. Somehow Ramanujan split into several souls.

too many integral-lovers present already.

Well, that's not the only thing you need to know, @Balarka. But perhaps it's the main thing (and orthogonal complements) you've not thought about. You need spectral theorem and canonical forms for linear maps and bilinear forms.

horcruxes, @Jasper? :P

I don't think so, @Jasper, but ok.

@BalarkaSen I dunno what that is.

@TedShifrin Yes, I will proceed systematically. I have learned this lesson finally.

@JasperLoy nevermind about it.

@BalarkaSen You are still young, lots of time to learn. I am already an old dying man.

I wonder if I still have Mike on ignore ...

So, I miss the days of interesting math in here ...

@TedShifrin why were you ignoring Mike?

Because he was opining that winding numbers and their generalization to higher dimensions in differential topology were not worth bothering with :P

@TedShifrin I miss talking to Jonas and Old John.

I don't think I know Jonas. ... I miss Pedro.

@TedShifrin The ramble I saw later yesterday about poincare duality and inner product structure on cohomology rings also makes me feel better.

The character of this room has changed entirely ...

perhaps studying linear algebra won't go amiss entirely.

@TedShifrin What happened to Pedro?

Is it because I joined

Not inner product structure, really, @Balarka.

@TedShifrin Yes, and it is largely my fault. I talk too much crap.

@Sawarnik he has become a mod.

no, mr eyeglasses

I think I lower the average intelligence in here by a lot

@TedShifrin there was something about billinear forms. i don't care until i get to it and read it carefully :P

But I think some of the relentless homework pests have gotten rid of lots of us.

@BalarkaSen bilinear, not billinear, and bouquet, not boquet

yes, bilinear forms, @Balarka. But you should also study transversality and intersection theory of submanifolds. It's all very closely allied.

@ᴇʏᴇs Balarka can compensate for us all.

@BalarkaSen but mods like rob or gruber .. still come to chat..

alex doesn't come anymore.

I hardly ever see AlexG, either :(

well, rarely.

Maybe I should be a mod too, LOL.

@Jasper: You'd be mod 1.

@BalarkaSen well, yes :/

but he came here when he was a mod.

@TedShifrin wouldn't have imagined you and mike encouraging me to learn stuff way ahead of myself a few years ago...

@JasperLoy JC are my initials, then 574 is a number I chose but I can't remember why

:P

I consider myself more like a Nikola Tesla than a Ramanujan in all honesty

@ᴇʏᴇs You think I have 100 per cent chance right?

Hmm, no, not quite a Tesla...

Did we, @Balarka?

@teadawg1337 Nikola Tesla was a great guy.

@JC574 People with names starting with J are very likely to go mad.

Jesus Christ is good initials, I suppose, unless you're a non-believer :)

@TedShifrin well, manifold theory must be quite ahead of myself.

Not at all, @Balarka, but you must learn multivariable calculus and some multivariable analysis (i.e., my book you want for free).

@TedShifrin Well, he was crucified, not a good ending.

It's a better ending than some deserve, @Jasper.

No, I didn't mean you :D

People star too many darn things here.

@BalarkaSen Are you aware of his work?

@JC574: What's the algebraic curve question for today?

@ted Next month I will do something very hard to solve my problems, wish me luck.

@TedShifrin hahaha

@JasperLoy Yes

@TedShifrin I do actually have one as well

Of course I wish you luck, @Jasper.

Have you been back to the doctor, Jasper?

@TedShifrin well, your book is way too expensive for a poor guy like me.

Hmmm... I think it's better not to compare myself or others to the greatest minds of the past

@Balarka, email me sometime

indeed, @teadawg ... I hate how much that goes on here ... seriously.

Let's enjoy math, work hard, and do our best, and stop bragging and comparing ...

@TedShifrin Do you email copies of your books to some people sometimes?

@TedShifrin i will, but not now. i will focus and work hard on linear algebra right now.

@TedShifrin I have that if $D$ is a divisor on an elliptic curve, and $a$ is a point on the curve, then $l(D+a) = 1$, by using Riemann-Roch

Very rarely, @Jasper, very rarely. There are too many scoundrels out here.

whoa, slow down, @JC574. What divisor $D$?

cackles maniacally

And then you can put it on bookfi @Balarka ?

thanks @Ted.

:)

just any divisor of degree $0$ ?

@Sawarnik no

ohhh, did you say degree $0$ before? :D

@BalarkaSen oops.

@Sawarnik That would be unethical.

@Sawarnik If you think I am a pirating prat, you're mistaken.

@BalarkaSen but you do download for free..

oh sorry @TedShifrin no i didn't

@JasperLoy I know :)

I am going to sleep, good night everyone. I hope the gods will come to me in my dreams.

Do you think of elements of the vector space as meromorphic functions, @JC574?

night, @Jasper.

I will get hold of books that have already been pirated, sure, @Sawarnik. That doesn't mean I will upload every book I get hold of.

@TedShifrin yes, but I'm fairly new to all of this so i might be missing some understanding

I only download books that I've already paid for ... like baby Rudin. Or those that are posted freely (like my diff geo notes or Hatcher or ...).

That's fine, @JC574. The point is that only the constant functions are in that vector space. i.e., the divisor $D+a$ can't move.

But you didn't get to your question ?

@TedShifrin wait I don't see why just the constant functions are in that space, let me think and get back, just a sec

I respect the amount of work of the author put behind the books, but some of us just don't have the money. I try to buy hard copies if I can, though.

this may answer my question anyway

@BalarkaSen True.

For generations and generations before you, @Sawarnik, students took books out of libraries.

I did so myself for many years ... or borrowed a book from someone who had it. Now everyone thinks it's his right to "own" all the books.

I even bought Hatcher even though it's freely available.

I prefer to have hard copies of books, @Balarka. I hate reading off the computer.

I found that too, lately. But that's probably because I started reading, not skimming through the pages as I did before.

I'm getting rid of most of my library now, but I have kept many books for 40 years ...

@TedShifrin: What do you mean by get rid of? Sell?

giving to students, colleagues, gave one book to the library ... I may sell a few to a bookbuyer in Ohio.

I'm keeping about 4 boxes for me ... even that's too much, probably.

AH

I get it :)

the constant functions are in there for sure

and then there's no room for any others

do you know how to think of the projectivization of the vector space as the linear system in which the divisor moves, @JC574?

right :)

This is one reason it's so hard to "teach" in here or on MSE, in general. One never knows the background or the approach that the OP's taking ...

@TedShifrin I can't say I've thought of it that way, it might be that it has been mentioned. I know there's a 1-1 correspondence somewhere. I'm following loosely the book by Frances Kirwan

I don't know her book, although I'm sure it's lovely.

So I'm just saying I won't always know the right language in which to frame an answer to you, @JC574.

@TedShifrin sure, that's absolutely fine :) I'm just very grateful for the help you've given

is there anything you'd recommend me reading in particular?

I love Clemens's little book "Scrapbook of Curve Theory." Also love Griffiths's "Lectures on Algebraic Curves" (I think that's the title).

thanks!

@TedShifrin ah ok, so I've seen that the projective space $P(\mathcal{L}(D))$ is in one-to-one correspondence with the effictive divisors equivalent to $D$

there you go ... that's why they're called linear systems, because they're parametrized by $\Bbb P^r$ for some $r$.

aah ok

thanks!

@TedShifrin using posts, you can mention references and the reader can look there for background that they may not have. In chat, you have to adjust to what the other person knows.

Sure, @robjohn, but ideally one wants to engage at the level that the OP is at. Telling someone to read a hundred pages of Griffiths and Harris or of Stein may not be helpful. :)

@TedShifrin I wasn't thinking of telling someone to read a book. If that is the gap of understanding, then perhaps the person is not yet ready for the answer. (They can't handle the truth...)

Sometimes, it's not clear ... A student in my diff geo class has gotten through calculus and all our "intermediate" courses with C's but can't think beyond high school algebra formulas. I'm sure he appreciates the generous C's he got, but were we helping him, seriously? I can't see how he'll get anything but F's in the upper-level courses.

@TedShifrin my econ teacher mentioned upper contour sets today. I wanna learn Mord about those. Is this analysis? What book should I use? I want something more insightful than Rudin...

hey guys

cantor set we cover them in

measure theory

@TedShifrin I want to ask you a question

still around?

C is very bad actually

I would cry if I get a C

@KarimMansour In the US the marks go from A to what ?

@Ramanewbie F

I dunno I am in canada we here go by percentage

And there is no $E$.

@KarimMansour We often have percentages and just use the letters as shorthand for percent ranges

@ThomasAndrews Wuut ? So it is A, B, C, D, F ??

@Ixrec can I ask you topology question ?

easy Rama

@Ramanewbie in my experience, there usually isn't a D either

@Ramanewbie A+, A, A-, B+, B, B-, C+, C, C-, D+, D, D-, F

divide 100 by 4

They use percentages in China, too

Right, A, B, C, D, and F. @Ramanewbie

@KarimMansour I know bugger all about topology

5

I want to ask a question in topology !

In graduate courses there's no 'D' range grade usually

in most of my uni classes A was >90%, B was 80%-89%, C was 70%-79% and anything below 70% was effectively a fail, regardless of whether they bothered to distinguish between D and F

I think one should get B but ofcoz getting A in all of your courses is better

it is my personal opinion that basically anyone can manage straight B's with non-Herculean effort

the only time I got less than a B was a class where I bombed an exam due to both of my calculators breaking, and the proctor failing to provide a replacement

In the U.S. it's very easy to get 'A's

yeah

I am a moron and I get 'A's in all of my courses

lol @Ixrec bad day

the midterm I took sleep-deprived was peanuts in comparison

thats bad

I aced an exam and had like 98 avg before then after that went to exam sleep deprived

and I ended up bombing the final and getting 76 % and I got 87

in the end

the one I took sleep-deprived was in a super easy class (intro to macroecon iirc) and I actually got a decent grade on it (B maybe?)

so I got kinda lucky there

guys

I have a question

I have for a math class a project

I have finished it

Is it a topology question

no no I have answered myself that question @ᴇʏᴇs

now my question for this class I have two things

@KarimMansour Cool, I can never answer my own questions

first thing is that I need to product a math pdf file that includes my name etc

the second thing I want to produce math file that has

"math file"?

that I can type math symbols in

@KarimMansour Which LaTeX editor do you use

I will download MakeLatex now

I want my other file to include slide not pdf

you can edit recent chat messages by pressing the up arrow key like this

omg @Ixrec I didn't know that

its to me @ᴇʏᴇs

I probably only noticed because I'm used to Skype

which editor should I download @ᴇʏᴇs?

@ᴇʏᴇs by clicking on the arrow at the right end of someone else's comment (you only see it when hovering over their comment), it will link your comment to theirs.

@KarimMansour I use TeXnicCenter

@ᴇʏᴇs okay good I will use that

oh I have mac not windows

@KarimMansour Oh

mr eyeglasses, we don't have A+, D+, or D-. Do you have F+, too? :P

@TedShifrin What's the highest GPA possible at UGA

@StanShunpike: In multivariable, you study level curves/surfaces. But, ultimately, you probably want Morse theory to understand how you make up manifolds in terms of level sub- or super-sets.

Just 4.0, mr eyeglasses.

And most of the 4.0's go to the majors that give A's to everyone. :P

I usually see A+ = 4.3

grade inflation is absurd ... that's all I'm saying.

so what can I use to make slides show using latex any ideas?

there is a slide format for LaTeX. Also google beamer.

@KarimMansour maybe look at beamer

@TedShifrin I feel really guilty about my grades..it's like getting $100 for no reason which is nice but undeserved

where can I get it @JC574 ?

why, mr eyeglasses, you raking in A+'s? From what you keep saying, I wouldn't guess that.

@TedShifrin Yes, and I definitely don't deserve them

yeah, I don't believe in them. They should be only for a very rare, exceptional student. Once every few years, not 10 in a class. Sigh.

@KarimMansour have you got all the stuff to make Latex documents anyway? I use texmaker

I have no idea what your situation is, mr eyeglasses; I'm just saying that on principle.

@JC574 I just downloaded it

@TedShifrin My situation is that I'm attending a low-tier school that hands out grades like candy because they want to look good for more funding, I guess

@KarimMansour I think you just put in some specific code, try googling beamer tutorial or something

Hello @MichaelAlbanese

It's like I was bitching before, mr eyeglasses. I have a student in my diff geo class who's gotten grades he doesn't deserve (C's) all the way along. He's been fooled into thinking math is a reasonable major for him. It is not. It's not a kindness to give students grades they don't earn.

Hello @evinda.

heya @Michael :P

Hello @TedShifrin.

@MichaelAlbanese Do you study maths at a university?

I don't think of your school as low-tier, btw, mr eyeglasses.

@TedShifrin Yea, I really regret my entire academics because my grades tricked me into thinking I had sufficient knowledge to proceed with upper-level mathematics and now it's backfiring

Yes I do.

mr eyeglasses, with hard work you can earn an undergraduate degree in math, but graduate school ought to be thought about very, very hard. It's indescribably harder than undergraduate.

guten Abend, Herr Mann.

@TedShifrin I already have all the requirements for a math degree and I didn't even do that much, so I'm kind of upset I wasn't properly prepared for grad school since I didn't know what any of it entailed when I first started

maybe do some reading on yourself @ᴇʏᴇs ?

before going to grad school

@TedShifrin I'm thinking of maybe applying for a phd in the US at some point, i haven't looked into it much, but i understand the systems are different. Do most home students complete a masters degree before attending grad school for maths?

I think that is important @JC574

to do masters before phd

nope, @JC574 ... very few do.

in history, English, political science, etc., it's more common.

@TedShifrin really? that's surprising

in our Ph.D. program, a very few have an M.A. At top schools, it's totally not happening.

@TedShifrin You're saying in top schools they're less likely to have an M.A ?

yes, @JC574.

@TedShifrin is this because the content varies, so they will have covered more material at top schools?

here in canada we take MA first before phd