to get a sense of what i mean when it comes to grading, here's a rubric that one of the physics education research people put together. (i'm not one of those people, but i have been exposed to the mindset)

groups.physics.umn.edu/physed/People/Docktor/talks_papers/…

@BenjaminR That's why I say that is good to show to the student the true picture: also the teacher is vulnerable and sometimes doesn't know how to solve things.

yep 'twas just clarifying what I was agreeing with

Unfortunately, you don't have this luxury in lower division university classes, where other departments will make demands on your time. And you have to train your students to understand why this is valuable, or else you will get angry calls from parents which will not make your department leadership pleased. So much of academia, unfortunately, is about logistics.

I originally taught students with the expectation that they would have similar levels of success that I did when first tackling these subjects. After some experience, I think that is really a pipe dream. If you are a physics/mathematics PhD, very few of the students you work with will be at the level you were when learning the same thiing.

@Semiclassical lemme see

I think we could do a better job at showing vulnerability in classrooms, but I also don't think that any naïve approach at doing so will have positive outcomes.

where i got most of my teaching mindset, btw, is in teaching intro physics for a few semesters

and the problems you run into there are things which a physics grad student should be able to solve quickly and understand even faster

so less opportunity for vulnerability there. but there will be times where you say something wrong, and even in places you do understand well you have to be careful not to make it sound trivial

I was told to grade a problem a certain (leniant) way today even, and I just said "they'll either fail this or the next course".

The students were asked to prove that trace is a linear map.

Linear algebra is not a terminal course at your school?

$(aX+bY)_{ii}=a X_{ii}+b Y_{ii}$

Some wrote trace(A+B)=trace(A)+trace(B) and trace(cA)=c(trace(A)) as their proof.

(einstein convention, of course)

@Semiclassical I see.

@EricStucky What parents call lecturers/professors? They must be insane people.

More than you think, Ben :/

Well

The students are over 18, it's up to them to talk with academic staff

They call the department, actually

That is mental and infantilising

it's really pretty stupid, yes

Yep.

The parents of those parents would never have done the same for them!

It's a big circle of indulgence...

i had the advantage of teaching either intro physicists/engineers (i.e. people who had some understanding of math going in) or doing the physics for premed/bio majors

in which case they tended to be upperclassmen and more responsible for their own work

didn't mean there wasn't some idiocy, of course

@EricStucky Many of the students were math/cse or math education majors. The full undergrad str. of my university is complicated and I do not intend to learn it. Some of them are math majors who likely will not be admitted in to any gainful graduate study.

However said students may benefit greatly as human beings from their mathematical studies.

Ah, that is too bad :/

Don't discount those that aren't champions

(speaking as someone thoroughly ungifted/untalented at math, just a lover/hard worker)

@Semiclassical are your teaching lessons on youtube as the ones by Ted?

nah

i haven't done any lecturing

@Semiclassical Is it forbidden? I see.

it's just not what my jobs have called for

Gotcha.

@Semi That rubric is depressing.

I should try to get some exposure at that, though.

u16: If you're too early in school, you can't lecture, yeah. And many grad students don't want to lecture later because it's very, very time-intensive.

right. on the other hand, if you want to go into teaching then you do want to do it eventually so that you can be the instructor of record on a course.

tru

TAing is one thing, but it's not the same as having responsibility for the course as a whole.

@PVAL clarify?

Apart from some discussions I had with Ted in the past, he has nice lectures on youtube. That is to be objective.

I enjoy pretty much the vectors and problems with vectors, what I did much more in the past.

@Semiclassical I guess it seems like it would lead to many students who can solve 70% of every question getting the same credit as students who could solve all of 70% of the questions.

i really should track down his lectures on manifolds etc.

That assumes that there's such a thing as a student who could perfectly solve 70% of problems and not at all anything else.

@PVAL How's your stuff coming

i've never used that specific rubric myself, I should note. i have used something similar in the past, but that was the semester that I TA'd for the prof who runs the Physics education research group here

Well these students certainly exist in mathematics (students who do not learn how to solve any problem completely but give "rough approximations" and students who solve some problems fully and nicely but are unable to solve enough.)

@MikeMiller I've proven something in one case, that I can probably extend to more cases.

I think he was talking about your second category, pval :/

Well I've seen students like that as well.

@PVAL Good luck with it.

Who managed to learn a few concepts as they should (and perhaps at the pace they should have), but are forced to speed up (and learn less) either because of their calculation speed or because of previous background others students have had.

ah, found what i was looking for

I think have something that will work in another project (actually based on the paper of Lin I have to read), though I haven't written out many details yet. I think I can get lots of interesting examples of something I've wanted for quite a while.

@Semiclassical One crucial step in solving the problem is the simple observation that $\sqrt{2}-1=\tan(\pi/8)$

if you go here, you can find sample quizzes. at the start of each of them is the rubric the prof had us use

@PVAL That sounds exciting.

@MikeMiller These things are contact-type hypersurfaces in $\Bbb C^2$.

Huh, I guess I don't know any examples except for the truly obvious (ellipsoids et al)

ugh. i'm at that part of the day where i really really want to go home, but i need to get this thing setup to run overnight

@MikeMiller I think I can get ZHS^3 examples (or at least thats the goal). I'm unsure if any non-trivial of these were known.

I would be interested to see them.

@PVAL Does your construction work for eg the boundary of a Mazur manifold whose double is known to be $S^4$?

@MikeMiller The hope is for it work with some of those.

What about say $\Sigma(2,5,7)$?

no hope there.

Actually I can probably prove $\Sigma (2,5,7)$ can't be.

Certainly it isn't for the induced contact structure from the milnor fiber.

and I think the other contact strs on that thing are known to not have the correct homotopy invaraint.

What's the simplest example of one that works?

I don't have one yet.

I think what I am trying to do should produce them

I see. but I mean, do you have an example that you think will work?

I think (this isn't an ZHS^3) if you take the ribbon complement of the figure 8 knot connect sum its mirror and make the 2-h have sufficiently small framing.

When you say the ribbon complement you mean complement of the ribbon disc in $D^4$ I assume?

I mean the 2nd picture from the left in figure 1.22 here users.math.msu.edu/users/akbulut/papers/akbulut.lec.pdf

Ok, I see.

If theres any mods on can we talk in a private room i think i found a glitch.

Hello there!

Can someone help me with a conceptual calculus question?

I can certainly try

So basically I was deriving some of circular motion equations

alright

and in my attempt I got this: $dr = r\cos(d\theta)*\hat{i} + r\sin(d\theta)*\hat{j}$

where $ d\theta = \omega \, dt $

How did you get that? Try doing Implicit differentiation on x^2+y^2=r^2

@shaihorowitz geometric attempt: when we have a minimal variation of the position vector (dr) we get a minimal angle (d theta)

then I used the law of sines

@shaihorowitz how would we get a relation of time there? D:

the main question at the moment is

can I integrate the right side?

You would relate dy/dx to dy/dt and dx/dt, but It looks like you can integrate just would be messy. my word is not gospel integration in polar coordinates is not my strong suit.

these are not actual polar coordinates

I saw a russian guy on yt doing this like I did before. I want to know if the integral on the right side is correct.

oh, and r is a function of time

omega, theta and alpha are also funcs of time

Hello @AkivaWeinberger !! Do you maybe know when we have that imA=kerB, and we know that A is 1-1, if we have also an information about B?