They don't have to give notes, they just have to give proper lectures.

Academia at research university levels does not reward good teaching enough for the average professor to make the effort.

@TedShifrin No, this is actually a professor I think is seriously not fit to teach, not just someone I dislike because the exams are difficult or I don't like his lectures or anything of that nature

@ABeautifulMind If I were a professor I'd come to the class and build the whole lesson there with the students. I mean I'd create the whole material on spot using the creativity of the students, I wouldn't come to the class with the lesson already prepared (and possibly taken and repeated one billion times in other classes). The students received the lesson they would deserve, for that level. This is the kind of professor I would be.

@ʙᴀᴅᴀᴛᴍᴀᴛʜ Why do you say so?

You told me about him before, mr eyeglasses. Have you talked with the department head?

I would teach the student not to solve problems, but to be brilliant! Learn how to use your mind at the maximum potential, that's the lesson! Be creative, be the best in anything you do.

@JasperLoy During office hours he goes on movie websites and ignores his students that come in to ask questions, and during lecture he doesn't answer questions but just shakes his head in disbelief and says the answer is obvious then moves on, when clearly he skipped like 10 (difficult) logical steps in between statements

@TedShifrin I'm not sure which professor I told you about; I've had several terrible professors but this one is the worst of them all

There were students who disliked grad students being their tutors, saying they want someone with a doctorate, lol. Very superficial attitude.

@TedShifrin The first time I complained to the math chair about a professor who wasn't really teaching any of the topics designated for the course, he basically told me to deal with it

@ʙᴀᴅᴀᴛᴍᴀᴛʜ If complaining to the head of department fails, then complain at the next higher level.

@ʙᴀᴅᴀᴛᴍᴀᴛʜ Go all the way up to President of USA, lol.

@JasperLoy I am going to be gone after next year; I don't really want to make a big deal that may threaten my shots at getting letters of recommendation or graduation. Also don't want to be known as an academic snitch/crybaby for the rest of my career

@ʙᴀᴅᴀᴛᴍᴀᴛʜ I don't know what they are like, I would really need to see with my own eyes.

@Chris'ssis Students aren't as willing as you might think they are. Most of them, at least.

Short informal question: In the study of algebraic topology in calculating the fundamental group of a space $X$, we prefer to think in terms of open sets $A,B$ such that $A\cup B=X$ and $A\cap B$ is path connected (with $x_0\in A\cap B$). By Van Kampen, $\pi_1(X,x_0) = \pi_1(A\cup B, x_0)\cong \pi_1(A,x_0)*_{\pi_1(A\cap B,x_0)} \pi_1(B,x_0)$. I am having difficulty understanding precisely how to approach $*$ when it is not $*_{\{e\}}$ but instead a nontrivial group.

Hey guys

I wish I could study algebraic topology

Do u all have any textbooks for Ordinary Differentail Equaions?

As I understand, $G*H$ is the free group formed of "words" comprised of letters, each letter being an element in either $G$ or $H$, but when it comes to $G*_K H$ there is something to do with modding out by a kernel

Think of it in terms of presentations, @JMoravitz. You take the free product (which just combines the generators and the relations), and the amalgamation adds more relations in the form of the $\iota_1 \iota_2^{-1}(g)$ terms.

In particular if you have a nice generating set for $\pi_1(A \cap B)$, you only need to add relations corresponding to where that generating set maps.

@yswong Teschl's ODE and Dynamical Systems.

@JasperLoy always suggests super hard books :(

@yswong If you want something easy, Coddington's Intro to ODE.

@JasperLoy Why not Arnol'd :p

@ɧɿρρԹʅȝՇԵՐՎԾՌ Do you know how I feel when the kids I help tell me they wanna become like me? :-)

@ʙᴀᴅᴀᴛᴍᴀᴛʜ Arnold is a little handwaving.

@Chris'ssis That's because you're teaching individuals who are willing to learn

very different from teaching a class

@JasperLoy My dynamical systems professor is a little handwaving

He has too many hands.

@JasperLoy He literally waves his hands when he's doing a proof and skips some steps which is okay I guess since I can fill the missing steps in as an exercise

@Theorem I will look at it in a while

@robjohn A while is over. =)

@ɧɿρρԹʅȝՇԵՐՎԾՌ Keep in mind I'm just self-educated ...

That's not a problem

@ABeautifulMind there is an answer?

@ɧɿρρԹʅȝՇԵՐՎԾՌ Yeah, it is. It's not easy to make some kids fall in love with math stuff in the PC games age.

@robjohn I don't know.

@Chris'ssis But I don't see how being self educated or not changes any of that

@ɧɿρρԹʅȝՇԵՐՎԾՌ Well, missing pedagogy courses ... (and this is really important)

I don't know if those help a lot xD

Depends on the age of the kids

@ɧɿρρԹʅȝՇԵՐՎԾՌ Do you teach?

@ɧɿρρԹʅȝՇԵՐՎԾՌ 16-18

@BalarkaSen i'm a student q_q

@ɧɿρρԹʅȝՇԵՐՎԾՌ Yes but I know students who teach courses

@BalarkaSen Ugh... we don't do that here

@ɧɿρρԹʅȝՇԵՐՎԾՌ Oh, sorry

You don't have to say sorry lol

@ɧɿρρԹʅȝՇԵՐՎԾՌ Also do you realize you keep pinging @BalarkaSen lol He might get a little annoyed

@BalarkaSen Soorrry :/

@robjohn Thank you .

@I'mGettingThere I can't xD SE doesn't allow to many name changes in a short time

@I'mGettingThere But his name looks so cool :(

@I'mGettingThere You can still easily ping me though

@I'mGettingThere seems to be scolding everyone.

@ʙᴀᴅᴀᴛᴍᴀᴛʜ 乃ﾑÐ ﾑｲ ᄊﾑｲん

HAHA no wonder q_q

He does, right?

@I'mGettingThere A Beautiful Mind = Will Hunting = Jasper Loy

Does a pretty good Jasper imitation, too

I figure he's got Jasper locked in a closet, somewhere.

Yes, I remember Alec. I think he once flagged me for talking about gays.

Clear your cookies ??

Maybe he didn't.

@PedroTamaroff thanks

@PedroTamaroff what's $A_f$? The subring generated by $f$?

To me, talking about gay people is like talking about brunettes. Some are, some aren't-it's not exactly earth-shaking news.

@AlecTeal Someone must have really pushed your buttons

Once I was flagged for saying 'this chat is full of gays'. I was not being offensive. There were really many gays in the room then, lol.

I remember

It's like saying 'this chat is full of crazy people' which is also true.

I don't care if people are gay or not. Unless people want to go out with me particularly, why should I?

@ɧɿρρԹʅȝՇԵՐՎԾՌ Once someone got flagged for asking me 'How long is your banana?', which I think is fine. I have many bananas in the fridge.

@ABeautifulMind You're old enough to know what innuendo is. =)

@PedroTamaroff Yes, but IMAO, no need to flag. =)

How long is my banana...gimme a sec., I'll check.

What is the minimum age to be to sign up and participate in MSE?

13.

About 8"...but it's starting to spot.

This is a math lounge mon, not gossip about peoples sex life.

:D

Under 13, you need parental permission?

No, you cannot join.

This is the math lounge...and over here, we have the chemistry end-table....

If the budget was bigger we'd spring for the quantum physics patio set...but so expensive!

O____O

I didn't sleep for 36 hours ... (or so)

@Chris'ssis Why?

@ABeautifulMind I worked.

@Chris'ssis On accounting?

@Chris'ssis you worked for 36 hours in a row ??

@Ramanewbie No, definitely no.

@ABeautifulMind Also on some accounting, but more on some math.

I remember working for some time on a proof $\pi$ was transcendental. It was hard...

@DavidWheeler How many pages did that take you

I am going to bed.

Once I didn't sleep for about 60 hours and everything around me moved in slow motion like in Matrix. It's interesting the sensation you have.

@Chris'ssis That's bad for you :/ it's really hard to concentrate

@ɧɿρρԹʅȝՇԵՐՎԾՌ Kind of.

My heart beats very fast. I'm out for some sleep.

Sleep well

@ʙᴀᴅᴀᴛᴍᴀᴛʜ Oh it was only 5 or 6 pages-just dense. The proof actually showed more-if $\alpha$ is an algebraic complex number, $e^{\alpha}$ is transcendental. So, $e$, all of its (integral) powers are transcendental as well.

"Only"

It's really quite remarkable that this is even provable, since establishing the existence of any non-algebraic real number took some time to come up with, and most questions of transcendentality are "unknown", even though these numbers make up the vast majority of real numbers.

@Alessandro Yeah, you're overcounting a few.

You're on the right track though. Keep doing inclusion-exclusion, and you'll be able to do it.

No problem, @ɧɿρρԹʅȝՇԵՐՎԾՌ. :P

@BalarkaSen What is he counting?

Dearrangements.

so fiew posts in one full hour !

@BalarkaSen Ah, OK.

@JMoravitz Pushouts.

@Pedro I (finally) understood what the snake map does :P It was a bit obvious so I guess I am a little ashamed at not getting it in the first place.

@BalarkaSen The snake map is obvious...? OK.

Yeah, well, it takes a relative cycle in $H_{n}(X, A)$ and maps it to it's boundary, which is precisely a cycle in $H_n(A)$

You have to check that it's well defined and all, but this is essentially it.

And this even explaines when the snake map is zero and when it isn't (I computed the homology of $\Sigma_g$ with it).

@BalarkaSen Oh, that's a concrete example. I was thinking the general snake lemma for an exact sequence of complexes.

Ah, there you are @Exterior :P

ello

@PedroTamaroff Oh. That. Well, I never grokked homological algebra, so...

@BalarkaSen You first have to study homological algebra. ;)

I was just going to ask something about the computation. You said any cycle in $H_2(X, A)$ has boundary inside the boundary circle before

Yes.

@BalarkaSen Did you do the thing you set out to do this morning?

but a relative cycle (an element of $Z_2(X,A)$) merely has its boundary in $A$

the circle is the boundary of $A$, not $A$ itself

nice profile pic, @PedroTamaroff. Also, I distinctly recall you telling me you don't know algebraic topology :o

sorry, i was busy with squashing a few mosquitos :P

well, take a cycle in $B$ (recall that $B$ is the other bit of $X$ when you chop off $A$)

that has boundary inside the boundary circle.

that I agree with

but I don't think I agree that any cycle in $H_n(X,A)$ has boundary in the circle

well, for any general cycle, you are punching up the rest (the bit in $A$ minus boundary circle) to a point.

when you say cycle in $H_n(X,A)$ you mean an element of $Z_n(X,A)$, yes?

yeah

I take it you're using $H_n(X,A)\cong \tilde H_n (X/A)$

yes.

but it doesn't seem intuitive to me

for instance, take a relative cycle which "covers" $B$ and "half of" $A$

its boundary would also lie in $A$, but it would not be in the circle

how's that a cycle? it has nontrivial boundary.

it's a relative cycle

it has boundary in $A$

hmmmm

I'm not sure if I was clear though. Do you see what's bugging me? I see the snake map sends $B$ to zero, but what about the remainder of $H_n(X,A)$?

well, isn't the remainder sent to 0 also?

should be, since your calculation came out right. I just don't see how though

let's look at it's homology class.

I just described a relative cycle whose boundary is not a subset of the circle

i think the rest of H_n(X, A) should all have homology class [0]

you mean $B$ is the only generator?

mmhmm

ah, so we're using $H_n(X,A)\cong \tilde H_n (X/A)$ and also the fact $H_2(\Sigma _{g-1})\cong \mathbb Z$

not sure why the second one is needed [yes, the first isomorphism is what we need]

to know we only have one generator

uhhhh. why can't we just quotient out $A$ and be done with it?

probably you are right though

I'm probably missing something, but how would we know there are no other generators for $H_2(X,A)$?

i have no idea. would have to think about it :P

@PedroTamaroff Indeed. What's it about, in particular? Group (co)homology?

@MikeMiller Er, no. Let me think about it.

@BalarkaSen What is what about?

homological algebra. i have no idea what it is, except diagram chasing [!].

Love the new avatar, @Pedro

Now I won't get asked things by 13 year olds.

i am not 13, @Pedro

@BalarkaSen I didn't say you were.

Hahaha, nice avatar, indeed.

i see the relevance of the comment :P

it looks suspiciously like a voldemort who transfigured his hands into his eyes.

Watch Pan's Labyrinth.

you've been setting up a lot of ugly avatars lately, @Pedro :P

There's nothing ugly about the pale man.

@BalarkaSen Every monster is beautiful. Your pre-established notions of monster beauty are loathable.

@Mike i hope you don't mind if i don't think about the hairy ball problem just now. it's late and i am really very exhausted to do the thinking. i'll ping you rightaway if i find anything tomorrow morning.

@PedroTamaroff monster beauty. nice terminology.

Anyone got time to assist me with Integrating rational functions?

(by partial functions)

From the above, we see that sin is $\leq 0$ for $[\pi, 2 \pi]$

Can we say that $\sint \leq 0$ for $t \in [2k \pi+\pi, 2k \pi +2 \pi]$ ?

sin is periodic, yes

we periodically commit sins, sure, @David.

Every 2 pies, in fact

Is there an way to share problems easily?

I'd like some help with these integrals.

@Owatch You can use LaTeX

@DavidWheeler Ok, thanks :)

@Owatch If you're not used to LaTeX : make your formulas here, and paste the weird code at the top when you're finished, enclosed by one '$' on each side. That way we can see it (math.ucla.edu/~robjohn/math/mathjax.html)

I use Latex for $everything$ -just the word, though.

Alright

$\displaystyle\int_{}^{} \frac{x^3 + 4}{x^2 + 4}dx$

In this problem, I noticed the numerator was greater than the denominator. So I am required to perform long division and get a remainder before proceeding.

After doing the long division, I got a remainder of: $x^2 + 4$

$x^3+4-x(x^2+4)=4-4x$.

So $\dfrac{x^3+4}{x^2+4}=x+4\dfrac{1-x}{x^2+4}$

What

Is it not this: $\int_{}^{} x.dx + \int_{}^{}\frac{-4x+4}{x^2+4} dx$

I must have done something wrong as usual.

Yes, that's correct.

That was correct?

Okay

Well then that is where I am stuck.

$\int_{}^{}\frac{-4x+4}{x^2+4} dx$

I can integrate the other piece just fine.

But in this case, I am supposed to factor the denominator.

I cannot do that.

@PedroTamaroff Your avatars. You have gone nuts trying to solve RH.

I cannot factor out 4 either.

@Owatch Well, in this case you need to do somethin else.

I don't know what else to do. . .

This is how I am told to do them.

Well, what is the integral of $$\frac{x}{x^2+4}?$$

Note that $(x^2+4)'=2x$.

And what is the integral of $$\frac{1}{x^2+4}?$$

If you answer that, you're done.

You want me to split the numerator, then separate them?

The first integral uses $\log$, the second uses $\tan^{-1}$ also known as $\arctan$.

@Owatch Yes.

Why $\frac{x}{x^2+4}$ ?

@DavidWheeler Do you use any latex graphics packages?

You can't factor x from 4x+4

I'm not factoring.

I'm splitting the fraction with sums.

Oh

@ABeautifulMind No, I heard Tikz is good for diagrams, but I get tired thinking about it...

$$-4\frac{x}{x^2+4}+4\frac{1}{x^2+4}$$

@DavidWheeler The two best families of packages are pgf/tikz and pstricks.

I'm having a bad day

Morning, @AlexWertheim

@DavidWheeler Do you want to talk about it?

Hey @Mike. :)

I borrowed that line from Robin Williams.

I see.

Should I split both 'added' parts into their own integrals?

Integral is linear.

So yes.

I have done so.

Now I can move 4 out in front of the integral

s

What kind of movies do you like, @AlexW?

One of my favorite questions, @Mike. :)

I like movies which show people with mental illness.

Generally, my taste is in dark/"slice of life" movies, I guess you could say.

That is very vague.

What is dark?

Specifics?

I hate this.

I know what a slice of pizza is, but not a slice of life.

It's not much different than a slice of pizza.

I will go ask the instructor.

It seems Americans like using 'different than'. The British usually say 'different from'.

I prefer 'different from'

Where I live, we use the British.

@Owatch What is the derivative of $\log(4+x^2)$?

Haha, sure. Favorites probably are: American Beauty (favorite), Se7en, L.A. Confidential, Shawshank Redemption, Donnie Darko, 12 Angry Men. Many I'm forgetting :)

What is the derivative of $\arctan^{-1}((x/2)^2)$?

@AlexWertheim Geezis, I never watched any of them.

@Alex Gran Torino?

@ABeautifulMind You should go watch them, and only come back when you've done so.

Agreed that many of those are good.

You have many to watch then, Jasper :)

12 angry men is a must see

Great film, @teadawg.

My favourites are Good Will Hunting, A Beautiful Mind, A Walk To Remember, Step Up, If I Stay, The Covenant.

What about you, @MikeMiller?

I tend to prefer visually stunning, artsy things. I like surrealism. Three of my five favorite movies are "The Man Who Fell to Earth", "Synecdoche, NY", and "Stalker"

@MikeMiller Geezis, again I watched none of those.

@MikeMiller Have you seen The Grand Budapest Hotel? It's very artsy and stunning

I don't know if you would like them, @ABeautifulMind. They are not at all like your favorites.

Interesting. I can't say I've seen any of those myself. I'll have to watch them - I'm a neophyte to the genre.

Not yet, but I intend to.

How do you feel about Koyaanisqatsi, @MikeMiller?

Pretty but I didn't get much out of it other than that.

It was mainly high quality because of the Phillip Glass soundtrack, I think. :P

Hmm, fair enough. It's my only exposure to that kind of film. It's what I think of, at least.

(That is, if it's not actually part of the genre you're describing)

I dunno, I wouldn't really call it a genre. Just some characteristics of films I like.

I don't know if I would call it visually stunning, but there's a Korean film I really like that you might enjoy. It's somewhat artsy and borders on surrealistic. imdb.com/title/tt0423866/?ref_=fn_al_tt_1

My favourite Korean film is Sex Is Zero.

Sounds interesting, @AlexWertheim.

I enjoyed it a lot, @MikeMiller. Little dialogue but very engaging nonetheless.

Have you seen being john malkovich, or adaptation? Other movies by the writer of synecdoche.

Sadly, I haven't. Being John Malkovich has been on my list for some time. I like Spike Jonze's directing, too.

Some other good ones I realized I'd forgotten: Pulp Fiction, City of God, Leon: The Professional, American History X.

@AlexWertheim What about the Orchid movie?

@Pedro: which orchid movie? If you're joking, I've missed it. :)

Too much on my mind @ABeautifulMind

@DavidWheeler Same here.

Adaptation is about orchids, sort of.