Yeah, @Karl, more evident with more variables. Cool.

Trivial, @Pedro. Tag arbitrarily close to sup/inf.

@TedShifrin Agreed. The argument should be carried carefully, though.

Actually, I use the latter as defn and prove the former.

@TedShifrin I prefer Darboux's approach all the way.

Me too ... But Riemann shows up naturally in many application estimates.

Fava's influence is showing, haha

Not on me @Fernando :D

@FernandoMartin Spivak and Fava, I guess!

Spivak defines the Riemann integral as Darboux did.

Waaaaaay cleaner.

Yeah, I made him add the appendix on Riemann ....

@TedShifrin Oh. Look-at-that.

In the multivariable book I avoided Riemann sums completely :)

Maybe we should follow Dieudonne and start with Lebesgue :)

@Mike Heh, yep.

One of my colleague believes that ... But I asked him how to calculate them :)

All right. Busy day tomorrow in ATL ... g'night!

Calculate? Perish the thought!

Night.

Growl @ @Mike

night @Pedro

We develop the integral to know how it works, never to use it :)

Can someone lead me in the right direction?

What exactly do I need to solve this problem

(proof-strategy)

Interesting thing: there are two definitions of the Riemann Stieltjes integral, which are not equivalent, but are equivalent for the plain Riemann integral.

@Pedro?

@DonLarynx Just sharing.

@Pedro: It is interesting, but can you help me on my algebra problem? What do I need to know to solve this problem? I had a crappy professor.

I didn't self-study, depended on the course too much

@DonLarynx what do you notice about the coefficients?

@anon: $(x^2 + 4)(x+2) + 3 = 0$

@DonLarynx anon said coefficients.

I don't see how you get that anyway

but as pedro notes, I said coefficients

$2(x^3 + 2x^2 + 4x + 8k)$ @anon

what do you notice about 2,4,8,3 in the ring Z16?

@anon Howdy, there.

hello

I don't know what to do with them @anon

@DonLarynx huh?

I didn't learn anything in algebra

serious, i am dead lost.

describe Z16 to me.

it's the integers with elements $a mod 16 : a \in Z$

in particular .... which numbers are zero divisors?

2, 4, 8

0

mmhmm

so what do you notice about 2,4,8,3? you notice, all but one of them is a zero divisor

yeah, i don't see how the set of zero divisors with 3 are related, sorry. all knowledge, no insight. i suck

in particular, 8 annihilates all of 2,4,8 upon multiplication, but not 3 (as 8*3=8)

so if 2r^3+4r^2+8r+3=0 for some r and you multiply by 8, what happens?

I don't see what multiplying does here. What if I multiply by $0$? Can't that be a root?

but $r(0) = 3$

what happens when you multiply the equation by 8? what do you get?

surely you know how to multiply

you get $8 = 0$, but I don't see what that does @anon.

is 8=0 possible in characteristic 16?

nope

How does this show me it has no roots?

therefore, Z16 cannot be a subring

one person's basic facts are another person's alien magic - MO quote

I don't mean to rain on your parade here, but i thought I would be interested in algebra and I sincerely hate it due to the circumstances.

circumstances?

my parade does not allow access to other internet denizens

in particular, no rain shall occur

teacher that never has office hours; sucky *** book, she teaches it the wrong way

I depended on the course

unlike high school where all I did was read books

and this is what I got

@DonLarynx "the wrong way"

@Pedro: Everyone in my class agrees with me.

@PedroTamaroff ?

lol he logged off

What is "the right way" to teach algebra?

which algebra...the simple one or abstract?

abstract

crap

the teacher applying it over and over again so the student can have a good feel for it, and apply it in his/her own way

is that under applied mathematics? I know secondary ed math majors have to take abstract algebra

Instead

spends 5 minutes on 1 theorem

moves on to next one

oh yeah and half the class was number theory

oh yeah and she also never interacted with students

@DonLarynx That is on to you, not the teacher. You have to apply it over and over again.

Hi, off topic question: How is $Gal(\mathbb{Q} (2^{1/3},\zeta_3): \mathbb{Q}(2^{1/3}))$ a subgroup of $Gal(\mathbb{Q} (2^{1/3},\zeta_3): \mathbb{Q})$ when the former has 4 elements. Doesn't that contradict Lagrange?

@Pedro: For the third time, I depended on the course.

@DonLarynx Meaning?

hey sometimes the prof sucks bar none k. Look what's happening to my calc iv class...if he doesn't curve heavily, everyone is going to get an F. I AM NOT KIDDING

I thought the course would lead me down the path of greatness. I always did her homework.

But it wasn't enlightening

the only thing that's encouraging me to practice it anyway is my classmate

In fact

@Pedro

otherwise I would've stick the finger at it

What's going on here?

We never learned about groups

@KarlKronenfeld People venting.

@KarlKronenfeld group therapy

We never learned about generators

(pun totes intended)

@anon HAHAHAHAH

calc is a sophomore level class...doesn't count towards the ba in Math so wtf am I in there? well if it wasn't for that class I would've been in trouble

Ah number theory without groups in an algebra course sounds a bit lacking.

@Karl: You think?

I wrote 3/4ths student on the enrollment form so I have to stick to 3/4ths otherwise I would've been screwed

In fact

permanently maybe

calc is sophomore AND doesn't count toward the major?

no

not at my school

it's a dead class...

calc i-iii matters... iv doesn't

oh, I see

@cap why do you think the former has 4 elements? it's a degree 2 extension, and the only automorphism is complex conjugation. in general if L/M/K is a tower then G(L/M) is a subgroup of G(L/K): every automorphism of L that fixes M pointwise must in particular fix K pointwise

so my mentality isn't there....the only way you'll ever get excited in calc iv is if you're going to be an Acturian'

which I'M NOT!

is it like multivariable II: MV harder?

yeah

to get in the BA Math program, Calc 1-3 are the requirements

and I passed that with B's

Analysis problems are nice and all, but there should be a limit

@anon: I have my algebra final in 7 hours

so if any a**hole like Ted wants to be a total B**** and says s*** like I don't deserve to be a Math Major, well f*** their negative crap. I've been through this twice already and prove those jealous haters wrong.

@usukidoll: Who's Ted?

that guy who was on here earlier

Ted SH...forgot his username

but he sucks :)

@usukidoll: You don't need to prove anything to anyone but yourself

@usukidoll: It is not worth burning bridges, mate

@usukidoll No need for that. I'm not defending Ted, but I think he was kinda cranky because of the result of his students in finals.

that proves how much he sucks :) or the students are lousy

@usukidoll: Focus on yourself, not on others.

whoa, what happened with ted? (lol@jealous)

ted went narley

radical

on me two days ago...all because I couldn't get the parametrize the surface integral thing corrected

anon is puntastic today

@anon usukidoll apparently had a problem on integrals.

And failed to solve it. Ted went bananas.

and he raged quit out of here for a while

Don't know about the context, usukidoll's attitude and else. @usukidoll care to provide the transcript part?

and came back

rofl

crap

I know that in such a ring we have no zero divisors

So they're all units

So I can just multiply by inverse

can you read that in your browser?

and get $g(x) = h(x)$

I can't even read your problem Don

chat.stackexchange.com/transcript/36/2013/12/6

@anon: Yes.

Didn't know it was that bad

I can read it (fwiw)

I'll fix it

we get white squares and whatnot

I bet he doesn't know how to sew a pair of shorts

pfffffffffffft

@anon fixed it

@usukidoll: More context

u mean where he ragequits out of here

I'm finding it >:D

@anon @karl @eric any tips?

oh right the algebra problem

looks

it's still kinda unreadable, for me at least

$f(x) \neq 0$

irreducibles generate maximal ideals in a pid.

@DonLarynx do you see why it suffices to prove there is an inverse for f(x)?

you see @karl, we never learned that vocabulary in my algebra class.

chat.stackexchange.com/transcript/36/2013/12/5/23-24 <-- where he rage quits

@anon because it will show that there does indeed exist a nonzero polynomial?

yes, if f(x) has an inverse, then for any h(x), we can set g(x)=h(x)f(x)^-1 and we get f(x)g(x)=h(x) (in F[x]/p(x) ofc)

what algebra text are you using?

@usukidoll: If you are letting words affect you negatively on the internet you shouldn't be on it. No hard feelings.

@usukidoll "If you're going to be a math major, you'd better have an attitude transplant."

That's not bad.

Let me link you

sucky book @anon

a sucky book with 4 stars?

@usukidoll I don't see how Ted is telling you there that you cannot be a math major or change majors or whatnot.

I don't even want to become a teacher

I've dealt with a history book with half a star and passed

For God sakes its so pedantic

it's in the transcript somewhere

and it is just...you want to die it kills your love for math @anon it really does

@usukidoll: Pedro is talking to you.

but I hate it when people tell me that...really I've been doing math since 2006...I've started at the BOTTOM man I want to get something out of this

I've seen it @Don

the TOC does seem rather .. strange

@usukidoll: I've been doing math since I was 5 years old. It's nothing to be prideful about. It's not a competition.

prefer watching 90s episodes of Soul Train than hear negative things

@anon what in particular?

That's what I keep on saying to myself...it's not a competition yet students boast too much about their 100s in an exam. ughhhhhh makes everyone feel bad. Of course I passed my exams, but what the hell man I used to take them without getting nervous. I scored like B's and A's during my community college years...what happened?

@usukidoll: Study smarter.

...

-________-

@usukidoll: If you don't like that answer. you will not improve.

how do it smarter then?

Um guys I have a question on proportionality, can anyone help?

Nick: Please, hold

@Nick Probably.

I am writing to @usukidoll

yo

Well, get off math.SE. Look at your calc iv book, open it. Hate it for the first 5 minutes. DO NOT LOSE FOCUS and do not close the book!! Then you shall read the first page. and then the second. you will have some thoughts telling you how boring it is. Then you will ignore those thoughts, perhaps you will think about skipping over the material. but you won't and you will think harder for about 10 minutes. and you will continue until you are hungry, or tired. then you can eat and sleep!

lol you know my differential equations book doesn't have a lot of practice problems. Hence I GO ONLINE AND SEARCH FOR SOME! :)

after dinner I'll be doing convolution with laplace

@usukidoll: if you do not get off math.SE and do your calc iv problems then it will not work. You will waste energy. That is all, I must go

is "hyperbolic half turn" a standard terminology in hyperbolic geometry?

I can't find it in my notes :(

I did some calc iv earlier

$$\frac{v^2}{2} + gz + \frac{p}{d} = \text{constant}$$ @Pedro: Does this in anyway indicate that $v$ is inversely proportional to $p$?

I even created a game called for every differential equation you solve you must solve a calc iv problem

seem to work

blast.....hate finals ... I just want vacation

What is Calculus IV? What does it include?

Calculus IV

Must be loads of integrals

"Multivariable II: Multivariable Harder" apparently

double integrals...triple integrals

lots of conversations polar cylindrical spherical

vectors

flux

stupid surface areas

divergence theorem is fun

Ohh. I get it now.

yeah that exam is first ughhhh

seems like calc 3 to me

but I did practice today and yesterday

along with my differentials

worst exam first is better than the alternative...

@Nick Not really.

Its good, the ugly things are over before.

just freaking the hell out...oh snap wait there is Mass formulas and inertias.

but those aren't hard

@pedro: aww snap =_=

Green's Theorem is cool

@anon maybe some miracle will happen and I get an $A$ in algebra

a $26/50$ was a $B+$ on the 2nd test

but $25/50$ a C on the first

consistently bad class averages (uncurved) are a good indicator of bad teaching methods

Yep I got a $C+$ on my advanced calc midterm (12 week midterm, first test!!!!) and the class average was a B I think

well it was a C

Half $A$ half $F$

lol

(for the most part)

well not really

looks at grade analysis

nobody passed the second exam in my calc iv class

lol

a $C+$ was $55/120$ on the advanced calc midterm but half the class got above a C+

actually

2/3rds

@anon so it's not my class's fault then... average on the second midterm was 28/72

I was the cutoff :p

@usukidoll: Yes.

I never understood that "curve" thingy you guys have over there, @anon.

curves are awesome

like if everyone failed the exams...it's not my fault :) and it happened twice in my calc iv class

@anon my professor gets her homework questions from online solutions.

XD. some of the classmates just use google to do their homework

they're that discouraged

I don't get letter grades

Why not just use the 55/120 as a grade?

@FernandoMartin Marketing, clearly.

@DonLarynx y are you typing yes?

@usukidoll it is your classes fault

@Fernando: 55/120 is undefined in the US of A.

We use letter grades

Why?

that makes no sense.

Because they are an epimorphism that is easier to understand

NOT EVEN >:O

you're creating drama

@DonLarynx That is not even half of all the work done. I cannot understand how that is a B.

curve curve curve curve F T W!

@Pedro: Here's the curveball: There's a curve.

@DonLarynx A curve. Aha. How does that work?

@Pedro: Not everyone is as smart as you. So for us mere mortals that don't have the purely mathematical mindset, we get curves so our egos aren't completely destroyed.

or just hop on the Soul Train

@DonLarynx I'm not judging or whatever, maybe getting 100/120 is nearly impossible, I don't know how the exam works. Maybe you're asked to do a part, like Ted did in his final. You can explain...!

It was my first time looking at advanced calculus, my second semester in mathematics. @Pedro, in order to not drop out of the major, my teacher curves because this material is not easy - and he knows it.

I think passing with a $B$ in advanced calculus given that criteria is superior.

then why not make easier exams?

@Fernando: Because the questions aren't that hard.

WHAT FERNAN SAID !! WOOP WOOP!

not unless you make it conceptual

Any moderators present?

then why curve the grades?

not sure why? @Potato

@Fernando: I just explained why.

This user is vandalizing his/her answers:math.stackexchange.com/users/17762/user17762?tab=activity

wow wtf...why all the edits

@Potato: OH SHIET

screenshot

he mad cuz he ain't invited on the Soul Train XD

@robjohn I have a moderation concern. This user is vandalizing their answers: math.stackexchange.com/users/17762/user17762?tab=activity

"Why should stack exchange benefit out of my answers"

what the fuck kind of question is that?

poorly executed as well

who wrote that?

@robjohn I have a moderation concern. This user is vandalizing their answers: math.stackexchange.com/users/17762/user17762?tab=activity

connection issues @Potato? you just posted the same thing twice.

user17762

Ah, it's somebody I know

not personally

@Eric: The devil.

He seems to be disgruntled lately

@anon Yes, my connected dropped for a second.

Sorry.

I hope he can get to a place where it works out :(

@EricStucky Yes. Check his profile blurb.

I told him " You need to have a transparent attitude in mathematics". Hope that works.

Don, his problem seems to be a little less about math and a little more about MSE. This is the post I saw earlier today that made me remember him: "Ping the moderators and you will get the following reply: "We are watching what we can to see if there is anything we can see that the script has not. Keep us informed.". But no action will be taken and they will keep watching till the entire site collapses."

I want some chicken katsu

Also, it'd probably be good if you watched your normative language a bit.

(irony observed)

Then why do we have sucky moderators? This is what happens when we have big government, some people expect others to do all the work - and then in the end, there is an overload of the system and everything collapses. Kind of like in "The machine stops".

Normative language?

Why?

I'm mildly put off by statements like "If you don't like that answer. you will not improve."

There's nothing wrong with that sentence explicitly

@Eric: it is what it is.

But it seems to be the beginning of a sort of unsavory personality

In what context did someone say, "If you don't like that answer, you will not improve"?

au contraire, more of a recovering one. ;) @Eric

Ah, I see :P

(@Potato: it's higher on the page)

(Don taking to usuki)

@Eric: I think the moderators do their job. However, I was assuming they didn't in response to your quote.

I don't really comment on the moderators, I just say "why if"

Fair...

but in my vocabulary, the phrase "why do we have sucky moderators" does imply that you think we have sucky moderators.

my usage*

yeah, I was assuming

Isn't that what happens when you assume?

I have no real reason to believe the moderators are bad.

(sorry, that wasn't directed at your last comment)

Well several other high-rep users have quit like Bill

eich

I'm trying to remember why Bill quit

My guess is that it was vaguely PSQ-related

Oh, no

it was moderators :/

also qiaochu unilaterally deleting questions in bulk iirc

I think the answer here should be undeleted and rolled back to the last version.

@Eric: I'm flustered, I don't like PSQ and answers in PSQs

Here is the revision history.

@MartinSleziak yes, we have been talking about that

some of the posts are being reverted

@Don: I doubt anyone likes PSQs per se.

I'm not sure what you're getting at :/

@Eric: Then why in that meta thread is it acceptable if no one likes it per se

Because sometimes we deal with things we don't like because they're beneficial to others...

Just venting

I mean, PSQs do clearly have a purpose

ohokay :D

@Eric: I will be done with algebra and I will be a free man forever, in 7 hours. Meanwhile I am looking forward to analysis final exam. Isn't that ironic?

Haha!

I've had a similar recent conversion from algebra.

So I feel you :)

@Eric: Care to tell?

Eh, same story, really

it's my second class

so I had a bit of background

and I was like "this is awesome!"

but then it wasn't :/

mainly because?

We'll see how long I stay away :)

Like I said, same story

no office hours

bad book, hard to understand lectures

What if we go to the same school...

haha, my teacher was male, though

oh lol

I had considered it :)

So you took the final?

Oh no

Our finals are at least a week away

Plus, I dropped that class

:P

I took the midterm. I got a 30/70 which was apparently a B- somehow :/

Didn't find out the letter until after I had dropped

Maybe I should have stuck through it...

gawd those grades look awesome

That was fun... I finished showing $\mathbb Q(x)/\mathbb Z[x]$ is not an injective $\mathbb Z[x]$-module even though it is an injective $\mathbb Z$-module--even a divisible $\mathbb Z[x]$-module.