In some classes @Karim I assigned a fair amount of homework. In differential geometry, usually only 5 problems per assignment, but the students still whined. In point-set topology, probably about 20 a week.

I'm getting about 15-20 per week in topology too

you know @TedShifrin what I used to do before I used to read every single line of DF including the examples now I just read the theorems and proofs and just go to problem solving.

it saves alot of time that way

well, examples in the text can be very illuminating

I think students who just do homework without understanding the text miss out a bit

@TedShifrin: It is raining here now. The forecast was for a lot of rain yesterday and none today. We got none yesterday and we are getting some now.

yeah I guess your right this week we have long weekend I can use it to catch up

It'd be great if I could assign students 30 questions a week.

Well, @robjohn, you know that weather forecasting is an exact science.

20 problems per week seems like an extraordinary amount for me

I am little bit lost in the part of solvable groups and nilpotent groups

I have always graded my own homeworks in upper level courses, so I don't want to assign more than I am willing to grade.

the prof rushed over it without really explaining them

In my honors multivariable math course, I assigned 10-20 WeBWork problems plus 10-20 proofs each week.

I wish I could have taken your class

@MikeMiller Did you delete your answer to the homotopy long exact sequence question? Both answers disappeared simultaneously.

you know our algebra instructor rushes over the topic

without really pausing

its grad class I guess

@PVAL: Oh, I'll put it back up. I guess John Ma deleted his because it was a dupe.

How much work do any of these proofs take?

are all grad classes profs rushes over the topic and let student just cover it by themselves @TedShifrin ?

For example, this week I got two problems for my Algebraic Number Theory Class, but both problems will probably take me an hour.

When you phrase a question like that you've already decided what the answer is.

I always did a nontrivial bunch of examples in my grad courses, @Karim, because I don't assume students can figure it all out for themselves ...

yeah exactly

I wish my prof do that

I decided many years ago I wasn't going to be like the average prof :D

he just talks to himself while writing on the board

Mine does that too

He agrees with himself and stuff

haha

yeah mine 2

if I don't read the book before attending the lecture then I will be lost

I suppose I could have been talking just to myself

You seem like you profess well in the YouTube videos at least

I have seen some of your videos

I like your teaching

do you really say "profess well"? :P

I still have to decide what to do tomorrow. Maybe I could just talk to myself, too.

@Karim an abelian group is a direct product of its p-primary components (so, sylow subgroups when it's finite)

try to prove that

Do I know anybody in your class, @Mike?

@Ted: Alex, and I think that's it.

Cool.

I've had about 15 students come to me with zeroes on a "proof" question claiming they had verbatim what I said the answer was.

@Chris'ssistheartist That matches the value of Mma10's closed form

@anon the way I was gonna prove it is that $G = P_1 ... P_n$, then construct an isomorphism between $P_1 ... P_n$ to $P_1 x P_2....xP_n$

just a lot nicer looking

I want to know how can I prove though

@PVAL: Well, things like reversing delta and epsilon in many students' minds is just "verbatim".

@robjohn hehe, yeah :-)

@KarimMansour go the other way

I usually don't write up complete arguments on the board, oftentimes saying some steps out loud with hand gestures. I've gotten complaints about this in the past.

ohhh yeah

your right

"But we just wrote what you did!"

Well, you have to model what you expect ... at least some of the time.

since if I do it the other way I directly get that $P_1 x P_2 x ... x P_n = |P_1| |P_2| ...|P_n|$

I don't really care if students do poorly because they didn't put any critical thought in what they wrote on the page.

@anon: How's things?

But we have to teach them HOW to write mathematics. They aren't born knowing it.

Even the grad students may not have gotten decent feedback as undergrads.

@MikeMiller great

(I had many UGA grad students who told me I was the first person to give them serious feedback.)

@MikeMiller whyyy that is one of the things I hate even in books saying some steps are trivial without actually showing it

Think we're talking about different things here. I'm referring to calculus undergrads where I skip some simplifications, jump through arithmetic, etc. Sometimes the grader demands more work than I show, and I think it's their job to put everything I said together.

oh ... ok

oh ok

@robjohn It's not a hard problem, but it's deceiving when looking at it, I did that in 3 different ways. You have fun working on it. Promise. :-)

One case I made a sign error at the start and threw the problem out of whack. Everything I did worked but got the wrong result. Figured out there error, told them where it was, that everything else would work out. They just copied down the boardwork and then the same comment I made about the error into their hw and figured that was acceptable!

Yea, since lectures are on a time constraint I wouldn't expect everything written on the board to always be complete proofs

LOL @ "They just copied down the boardwork and then the same comment I made about the error into their hw and figured that was acceptable!"

@TedShifrin When I have students asking for feedback at a lower division level, they are almost always grade-grubbing. They usuallu try to argue with me before I finish explaining what's wrong.

omg

@Chris'ssistheartist I will

yes, @PVAL, I've had that experience, too, plenty. Trust me.

@KarimMansour There's a point to which this is necessary. If you think D&F is long now, you should see it if they wrote out every single detail.

I would buy such a long book with every detail

I would never write it.

well they don't really have to show every detail but atleast the details which isn't really trivial and they say it is obvious

Students MUST read math texts with pencil and paper, and work. This is why my linear algebra book gets trounced by students on Amazon. They expect it to be a high school/calculus book.

@KarimMansour They don't know how every reader thinks. They probably can't see why it's not obvious to some people

One of my fav. books in my field requires me to spend a lot of time staring at most pages to figure out all the details. It's also already 400 pages. I also think one benefits from the struggle.

It'd be nice if I had time to give individual written feedback to all students, but I have to grade 120 quizzes weekly as well hold two lectures for them (calling a 120 person class a "discussion section" doesn't sit well in my gut). Also D&F has plenty of details written out in that book, for the well-prepared student reading that book should not be much of a chore.

120? Holy crap.

yeah I guess your right, since when you struggle with the text you get most out of it rather than having everything given to you on gold platter.

Do you not have student-assistants at your uni?

Our school system doesn't have TAs either

lol

he is the student assistant!

haha

?!

So what does the professor do?

If he is holding the lecture

@Krijn I am holding "discussion sections" which happen to be filled with 120 students.

That's barbarism.

But our society doesn't respect education and certainly in places like GA and TX and WI they don't want to pay for it.

Well we do have the highest paid academic mathematician in the world. Guess I just have to wait for it to trickle down.

Grad students here get paid $6,000 per semester to teach 2 sections (they prepare the lectures and grade everything)

@anon yeah your right the other direction is easier. $|G| = p_1^{\alpha_1} ...p_n^{\alpha_2}$, since each suppose that $P_i$ is the sylow p subgroup for the ith prime divisor of G. Since each subgroup of abelian group is normal so in particular $P_i$ is normal, so $n_{p_i} = 1$ for each $i \in \{1,...,n\}$. Now consider F = $P_1 x ... x P_n$, $|F| = |P_1||P_2|...|P_n|$, since we have $P_i \cap P_j = 1 \forall i,j \in \{1,...,n\} \ with \ i \neq j$

Oh, who's the highest paid in the world?

mr eyeglasses, that is slave labor, literally.

$|F| = p_1^{\alpha_1} ... p_n^{\alpha_n} = |G|$, so F = G.

@morphic what country is that ?

@TedShifrin I think its Luis Cafferelli (or hes close to the highest whose salary is available publicly) (400k and change)

@PVAL: Terry beats him, he pulls in 500, and I think that's before grants.

wow ... I had no idea in either of those cases.

I thought Terry was 300k

Let me check.

I clearly was an incompetent fool :D

@KarimMansour USA

I got no idea after grants.

Regular pay 387, gross pay 518. I assume the latter means in addition to pay coming from grants.

Eh well its a lot in any case

Holy f*** ... I quit. Oh wait; I already did.

I wouldnt even know what to do with all that money

Looking through berkeely salaries: there's a custodian whose reg pay was -65$

Our secretary in charge of budgets for faculty grant proposals, etc., was at one point about 10 years ago barely making $22K.

it's Will Hunting

Ian Agol only goes home with 200/yr. Poor guy.

Well here its easy to spend it. You fund grad students so they don't have to teach 120 student discussion sections.

I bet StationQ pays better than UCLA

Surprised, berkeley faculty seems to be less paid than LA.

I retired at $100K, after 34 years. Sigh :P

Station Q is probably a nice job.

Freedmans the director too. That's got to be a lot.

@PVAL: Is Hanselman a new hire?

He's a postdoc who started last year, and I think hes gone after this one.

I see. He's doing interesting work.

If I'm the one who started this, I apologize.

Don't, I'm sure you've committed worse atrocities.

Gee thanks, asshole :)

How come Luis Caffarelli makes so much?

He invented the notion of PDE, revolutionizing mathematics

Excuse me?

He invented it? Wow

What else could justify that salary?

Nonsense, mr eyeglasses

I should go back to the salt mines.

You know how when you pour water out of a bottle into a glass.

If Cafferelli's fundamental work in fluid dynamics wasn't done all your water would end up on the floor.

LOL ... I guess they weren't pouring water or wine into glasses the last century.

Or into mouths

I don't think the caveman needed Sobolev spaces.

Hmm, if I'm working in a Dedekind domain, and I know the factorization of ideals $(A)$ and $(b)$, is there an easy way to find the factorization of $(a,b)$?

I thought $(a,b) = (a) + (b)$ would work, and $(a) + (b) = (gcd(a,b))$\

@Krijn write out an explicit formula for the prime factorization of gcd(a,b) in terms of the prime factorizations of a and b. then use the formula again, but with prime ideals.

Yeah just taking the minimum of the valutaion works, I guess

that applies for adding any two ideals in a dedekind domain

valuation*