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Physics is my life
Physics is my life
3:12 PM
Ok.@Fargle thanks
 
satan 29
satan 29
hey everyone.
 
Physics is my life
Physics is my life
Hey@satan29
 
satan 29
satan 29
Let w = f(u, v) satisfies the Laplace equation wuu + wvv = 0. If u =1/2 *(x^2-y^2)

and v = xy,

then show that w also satisfies the Laplace equation wxx + wyy = 0.
 
Physics is my life
Physics is my life
For the domain and range of f(x-3)+2 , why is its range = 2,infinity and domain real numbers
Range should be only till 2 right
 
Fargle
Fargle
@satan29 Use the chain rule. You can write dw/dx (curly d's), in terms of dw/du and dw/dv, and similarly dw/dy can be written in terms of those. Extend this to the second derivative and you should be able to get from one fact to the other.
@Physicsismylife That depends on f.
Does the problem give you f(x), or what f(x)'s domain and range are?
 
satan 29
satan 29
3:26 PM
i used the chain rule, and managed to prove it. However, it got very tedious... I was wondering if there was a better/ more elegant way to approach this...
 
Physics is my life
Physics is my life
@Fargle
It only says y = f(x-3)+2
thats it
The range answer in my book is 2,infinity
 
Fargle
Fargle
There has to be some information about f somewhere. Otherwise the question is ill-posed.
@satan29 There might be---I don't know any, but I'm hardly an expert.
 
Physics is my life
Physics is my life
It says to domain range graph of y = f|x-3|+2
I think I mistakenly didn’t write this
it is mod as well there
@Fargle that’s it
 
Fargle
Fargle
Wait, is f just supposed to be a constant? Or is it just not there?
 
Physics is my life
Physics is my life
I am new to this topic.I am not getting what you mean
I have posted the exact question now
I found the graph but not getting domain and range
@Fargle I am sorry but it is this much info only
 
Fargle
Fargle
3:30 PM
What I mean is, is it just y = |x - 3| + 2?
The f is really throwing me for a loop here.
I have no idea what that's supposed to be---I'll pretend it's a constant.
 
Physics is my life
Physics is my life
Ok.wait they have written the question wrong
Yes m you are right
there is no f
 
Fargle
Fargle
Alright, phew, haha
 
Physics is my life
Physics is my life
in solution , they have written f
but in question they have
sorry @Fargle
 
Fargle
Fargle
No problem.
 
Physics is my life
Physics is my life
@Fargle ok so where am I wrong
about range part
 
Fargle
Fargle
3:32 PM
The range is [2, infinity) because the range of |x| is [0,infinity).
That is, |stuff| is always >= 0. Therefore, |stuff| + 2 is always >= 2, so it must be in [2, infinity).
 
Physics is my life
Physics is my life
Ok.
is it right to write this f|x-3| = |x-3|
It is in my book
then it written that f|x-3| +2 =y
 
Fargle
Fargle
I don't personally know how to make sense out of it so I wouldn't say it's right. Unless there's some misunderstanding here, I think that has to be a typo in your source
That f being there, that is
 
Physics is my life
Physics is my life
Ok
Why is it wrong ?
 
Fargle
Fargle
3:48 PM
It's just that it's very weird. To say f|x - 3| = |x - 3| is just to say that f(x) = x for nonnegative x. I don't know why they'd be so roundabout with it, particularly if they didn't say anything about f
 
Ryan Unger
Ryan Unger
4:29 PM
@BalarkaSen how am I reading it?
@BalarkaSen thx
There are multiple things I don't understand in that gromov paper
 
robjohn
robjohn
4:44 PM
@Physicsismylife is it that or is it $f(x-3)=|x-3|$?
 
user2103480
user2103480
5:40 PM
@Semiclassical btw, fourier-transforming back is no problem with wolfram alpha for that fractional laplacian formula we talked about
just have to take one step back and only fourier-transform $|\omega|^{2\gamma} = -\sqrt{\frac{2}{\pi}} \sin (\pi a) \Gamma(2 a+1)|t|^{-2 a-1}$
then it's "just a convolution" of this with the function in question
goddammit this prof said we don't need any PDE pre knowledge and then he's all like "yeah this fractional laplacian with dirichlet boundary conditions"
Every time I google these things it's further into the rabbit hole
 
Mats Granvik
Mats Granvik
6:07 PM
Leibniz is a person invented by the cookie company to increase the sales of cookies.
 
Astyx
Astyx
They should add Leibniz in Cookie clicker
 
Edward Evans
Edward Evans
6:19 PM
Christ cookie clicker
 
Physics is my life
Physics is my life
@robjohn it is right what you wrote
 
robjohn
robjohn
@Physicsismylife That makes more sense.
but it still means $f(x)=|x|$
 
BigSocks
BigSocks
so like what is the difference between a cofiltered limit and a filtered colimit
 
Astyx
Astyx
I'd say they're dual to each other, but I don't know anything
 
BigSocks
BigSocks
yeah that was my guess too but
it seems like more than just duality
like adjunction + duality somehow
 
user2103480
user2103480
6:30 PM
@Astyx no a cofiltered limit is dual to a cocofiltered colimit
 
Astyx
Astyx
sounds tasty
 
user2103480
user2103480
yes
cococofiltered cocolimit
 
Astyx
Astyx
I'm in love with the coco
 
user2103480
user2103480
cocofiltered cococolimit
@Astyx legend
but then you're just in love with "the"
 
BigSocks
BigSocks
with the $(-)$
 
Astyx
Astyx
6:32 PM
Someone should edit the audio and just cut the sound at appropriate places
 
BigSocks
BigSocks
what category theorists hear
 
user2103480
user2103480
cocone is the worst term ever
I pronounce it as "cocon-è" out of spite
 
BigSocks
BigSocks
lmao
?
 
user2103480
user2103480
yes thats just a meme name
category theorists are serious
coco-mplete
 
BigSocks
BigSocks
some would say category theory is a meme
 
user2103480
user2103480
6:35 PM
covid is really a thing
you work alone on a course
have problems with it
 
BigSocks
BigSocks
if vid is life, covid is death woah
 
user2103480
user2103480
have no one to ask
write an email to the prof
get no answer
rip
 
BigSocks
BigSocks
oh yeah, that sucks, man
 
Astyx
Astyx
yeah it really sucks
 
BigSocks
BigSocks
if it weren't for you kindred spirits in this chat helping me with intro arith geo and alg geo I'd be way sadder
 
Astyx
Astyx
6:37 PM
Then again, if it weren't for Covid I wouldn't have reflected so much on the reason I'm studying in the first place
 
Thorgott
Thorgott
dunno, a cofiltered limit is a filtered colimit in the opposite category
 
BigSocks
BigSocks
cool well that's good then
 
user2103480
user2103480
although I'm regularly surprised at how much analysis the people here know besides their actual area of focus, the focus is on geometry, topology and number theory here so this chat is more motivational lol
(to me)
 
BigSocks
BigSocks
so a pro-object of a category $C$ is a formal filtered colimit of objects of $C^{op}$
 
Astyx
Astyx
I've done a whole lot of analysis before this year
I probably should have continued in this direction tbh
I wouldn't be failing so hard
 
BigSocks
BigSocks
6:39 PM
what changed your mind?
 
user2103480
user2103480
@Astyx it got apparent when I asked about the pde stuff
yeah, why did you "switch"
 
Thorgott
Thorgott
@BigSocks not like that makes anything more transparent, but yes
 
BigSocks
BigSocks
not at all I think it makes it much worse if anything. But I, this morning, just wanted it to be a filtered colimit. so I am happy
 
love_sodam
love_sodam
could you people recommend advanced linear algebra text? I studied Hoffman's textbook and currently reviewing linear algebra
 
Balarka Sen
Balarka Sen
Algebra is immoral. Algebra is obscene
 
user2103480
user2103480
6:49 PM
@BalarkaSen my topology lecturer rejoices every time we prove an algebra result by topological means. I can only explicitly remember FTA but I think there were 2 or 3 other examples
 
Thorgott
Thorgott
subgroups of free groups are free, probably
 
user2103480
user2103480
some day he'll say "by PURE TOPOLOGY"
 
Thorgott
Thorgott
 
Balarka Sen
Balarka Sen
That is a good proof of course
 
uriyaba
uriyaba
Hi, why am I getting downvoted on a correct and helpful answer I had provided?
-1
A: Combining 2x1 mux and 4x1 mux with AND gate

uriyabaYour answer is incorrect, since when computing the output of both multiplexers, you incorrectly took into the account the dependency of the output on the selector / selectors. Watch closely how I did it and compare to the results you got! According to the truth table of a 2x1 mux and a 4x1 mux, w...

I know this isn't the EE chat, but no one is online in there, so I figured I'd ask here
 
Thorgott
Thorgott
6:59 PM
of course you would say that, Balarka
 
Astyx
Astyx
@BigSocks Curiosity. I thought I could handle advanced courses in topics I wasn't familiar with. I probably would have if it weren't for Covid
 
Thorgott
Thorgott
Day 1: Curiosity.
Day 100: caRTiEr diViSoRs
 
BigSocks
BigSocks
lmao
I am at day 20something then. looking forward to it
and I get that @Astyx ... covid just drained me of motivation for about 10 months and my brain kinda wiped. was just trying to survive mostly
can't imagine actually having responsibilities in courses atm
 
Astyx
Astyx
I mean, I learned a ton of stuff and find it mostly interesting
It's not wasted
 
Thorgott
Thorgott
Day $H^1(X,\mathcal{O}_X(-D))$
 
Balarka Sen
Balarka Sen
7:05 PM
lol shut up thorgott
 
Astyx
Astyx
I'm taking a course in arithmetic geometry next semester to combine what I learned in AG and ANT
 
Thorgott
Thorgott
balarka still salty that i DESTROYED him on hyperbolic geometry
 
Balarka Sen
Balarka Sen
@Astyx lmao uh oh
@Thorgott friendship abandoned with hyperbolic geometry; parabolic geometry is now my new friend
 
Astyx
Astyx
This will be regular AG (not scheme theoretic) so it'll hopefully more down to earth
btw I (finally) watched the first episode of Twin peaks
Looks cool
 
BigSocks
BigSocks
oh that's good. the scheme theoretic stuff does seem cool though. do you think you'll do it one day?
and it seems a reasonable path the one you're taking
 
Astyx
Astyx
7:11 PM
lol the scheme theoretic stuff is what I've been doing for the last 4 months
 
BigSocks
BigSocks
ooooh lol
 
Balarka Sen
Balarka Sen
@Astyx its awesome
 
Astyx
Astyx
I have $200^{15}$ scheme related definitions in my head and no use for any one of them
 
Semiclassical
Semiclassical
@user2103480 ah nice
 
BigSocks
BigSocks
lol what? no use? isn't it the way to do AG and what follows?
 
Astyx
Astyx
7:13 PM
I have no use for AG
 
BigSocks
BigSocks
oh you're pretty set on analysis then
 
Astyx
Astyx
No idea why it's relevant
 
Balarka Sen
Balarka Sen
@Astyx good man
thou hast seen the LIGHT
 
Astyx
Astyx
@BalarkaSen I've also been watching TheSerfs' stream
 
Balarka Sen
Balarka Sen
lmao nice its one of the better channels
 
Astyx
Astyx
7:14 PM
which completely fucks my sleep schedule
 
Balarka Sen
Balarka Sen
haha
 
Astyx
Astyx
ye it's fun
 
user2103480
user2103480
7:27 PM
@Semiclassical lol I wrote equality there but I think you knew what I meant there
polish research team

polish research team
 
Astyx
Astyx
lol
 
Thorgott
Thorgott
lmao beautiful
should letterbox it and put the caption on it, should sell for a good price on the market
 
user2103480
user2103480
deep fried
sell it on the darkweb meme market
 
Thorgott
Thorgott
not sure if it that's fryable, should definitely add an artificial ifunny watermark tho
 
Astyx
Astyx
Ofc it's fryable
add crying emojis
And everything becomes fryable
 
Thorgott
Thorgott
7:41 PM
sure, I suppose crying emojis always work
but I don't think any of the finer visual deepfrying techniques would have much of an effect given it's not that visual a meme
hmm, or maybe it's worth a shot
 
Alessandro Codenotti
Alessandro Codenotti
@Astyx nobody does
 
Astyx
Astyx
idk you could make a rainbow background as well
And put a B token to replace the P of "polish"
@AlessandroCodenotti Then why is everyone doing some?
 
Alessandro Codenotti
Alessandro Codenotti
@Astyx sunk cost fallacy
 
Astyx
Astyx
lol that explains it
"I've invested so much time in understanding it, I need to pretend it's useful otherwise my mind will collapse"
 
Balarka Sen
Balarka Sen
@user2103480 loool
are all those the same people
soon i'll publish a paper coauthored by balarko, bolarko, balorko, arko and myself
 
Thorgott
Thorgott
7:56 PM
im gonna publish my joint work together with khorgokk
 
EM4
EM4
preqs. for topology are what? Is it mostly set theory.
 
Thorgott
Thorgott
inasfar as one considers set theory to be a prerequisite to any kind of classical mathematics, otherwise none
you should know choice principles if you wanna learn Tychonoff's theorem, but that's about the only thing
 
user2103480
user2103480
8:13 PM
@BalarkaSen lal
 
EM4
EM4
C = {0} $\cup$ (1,2) find the limit points.
are the limit points contained in [1,2] ?
 
user2103480
user2103480
@Astyx ooofff we're treating memes like math
just throw all the usual tricks onto it
 
Ryan Unger
Ryan Unger
8:49 PM
@BalarkaSen $|x-y|+\sqrt{|t-s|}$?
 
user2103480
user2103480
Anybody know how $e^{X^2}$ works for centered gaussian $X$
ah I can actually compute that wow densities exist
why do I sit on this for so long and then as soon as I ask I remember
 
Astyx
Astyx
Happens to everyone
The real help of chat is letting you actually ask the question, not the people answering it
 
Ryan Unger
Ryan Unger
I ask my roommates things they probably won't know the answer to
and about half the time I figure it out just by asking
 
Astyx
Astyx
It's the rubber duck syndrome or something
 
Ryan Unger
Ryan Unger
yeah
 
copper.hat
copper.hat
8:54 PM
@FakeMod yes, it is diffeerntiable.
 
user2103480
user2103480
@RyanUnger people tend to misunderstand when I ask them about cylindrical wiener processes
probability brain
 
copper.hat
copper.hat
the urge to flag is almost unbearable...
 
user2103480
user2103480
math.se chat brain
 
Thorgott
Thorgott
9:18 PM
hey @user2103480
 
user2103480
user2103480
hello there
 
Thorgott
Thorgott
are you here? i wanna post sth real quick and then delete
 
user2103480
user2103480
there!
looooooooool
saved it
 
Astyx
Astyx
perfection
 
Balarka Sen
Balarka Sen
this is what you've been doing for the past few hours?
 
Astyx
Astyx
9:21 PM
I would love the rainbow background tho
 
Thorgott
Thorgott
@BalarkaSen no, I also did some algebra, though same level of productivity ig
@Astyx that technique is too advanced for me
 
Astyx
Astyx
Could also have added text distortion to emphasize the funny part of the meme
But it's very good as is
 
user2103480
user2103480
do I have the rights to post that to >implying we can discuss physics on fb
 
Astyx
Astyx
👌
 
Thorgott
Thorgott
lol feel free
 
user2103480
user2103480
9:25 PM
the deep fried aggressive laugh cry emoji cracks me up
 
Thorgott
Thorgott
I'd love to have had some distortion effects, but I don't actually know how to do picture editing beyond copypaste and applying random filters
the latter two get you far enough in life
 
user2103480
user2103480
wise
 
Thorgott
Thorgott
the ok sign was very bad in hindsight, gets killed too much by the blur
 
user2103480
user2103480
dont overthink it
it is sehr gut
 
Astyx
Astyx
the deep fry being unreadable is what makes the meme authentic
 
Balarka Sen
Balarka Sen
9:29 PM
this chat is too intellectual for me
discussing the aesthetics of deep fry
 
Semiclassical
Semiclassical
i'll stick with the aesthetics of random video game music
 
Thorgott
Thorgott
yeah, I think the balance between being filtered into unintelligibility, yet still intelligible enough to maintain the essence of the non-meta layer of the joke works out fairly well
@BalarkaSen always has been
 
Balarka Sen
Balarka Sen
lol
 
Fargle
Fargle
"Can I get a uhhhhhhhhh intelligible meme?"
"sense machine broke"
 
Semiclassical
Semiclassical
i should be doing admin stuff (putting together my google calendar for the semester, getting zooms links set up, emails etc) but my brain is just sorta saying..."sorry, out to lunch"
 
user2103480
user2103480
9:35 PM
goddammit finally I almost solved that damn exponential of norm of stochastic integral exercise
 
Semiclassical
Semiclassical
that sounds both interesting and frustrating
 
Astyx
Astyx
@Semiclassical random as in generated randomly?
 
Semiclassical
Semiclassical
random as in "i have no good way to introduce this into the conversation"
 
Astyx
Astyx
Ah ok lol
Cool music
 
Semiclassical
Semiclassical
yeah, though rez is known for that
 
user2103480
user2103480
9:38 PM
and I have NO clue at all why but apparently $$\mathrm{tr} \log(1-2\varepsilon T) = \sum_{n \in \Bbb N} \log(1-2\varepsilon \lambda_n)$$ for eigenvalues $\lambda_n$ of nonnegative self-adjoint operator $T$ of finite trace
 
Semiclassical
Semiclassical
something something $\ln \det = \operatorname{tr}\ln$?
 
user2103480
user2103480
not a clue man
 
Semiclassical
Semiclassical
that's an identity, actualy: $\ln\det A=\operatorname{tr}\ln A$
 
Astyx
Astyx
that seems reasonable
 
Semiclassical
Semiclassical
and i think it immediately gives your identity, in fact
 
Astyx
Astyx
9:40 PM
You don't really have to use this equality though
 
Semiclassical
Semiclassical
?
 
Astyx
Astyx
It's just the expression of the trace in a base of eigenvectors
 
Semiclassical
Semiclassical
ah, yeah
 
Fargle
Fargle
Wow, I had never seen that identity before but it makes sense. $\ln \prod \lambda = \sum \ln \lambda$
 
Semiclassical
Semiclassical
yeah. for diagonal matrices it's obvious
 
copper.hat
copper.hat
9:41 PM
not a surprise from finite dimensions.
 
user2103480
user2103480
I had to figure out that $\int_0^T\Phi_s \, \mathrm{d}W_s$ is gaussian on a Hilbert space with covariance operator $\int_0^T \Phi_s \Phi_s^\ast \, \mathrm{d}s$, for which I had to prove that all the hilbert-schmiddity, nonnegativeness and trace stuff is conserved under bochner integrals and
 
Thorgott
Thorgott
"schmiddity"
 
Semiclassical
Semiclassical
get schmiddity
 
copper.hat
copper.hat
wid it
 
Fargle
Fargle
Is this taking $\ln A$ to mean "the matrix $X$ s.t. $e^X = A$" rather than just component-wise ln?
 
Semiclassical
Semiclassical
9:42 PM
yes
 
Fargle
Fargle
Okay---I see now that it was a silly question, componentwise ln would be nonsense
 
user2103480
user2103480
Man I said before I have no clue, I still don't know what that logarithm operator actually does
 
Semiclassical
Semiclassical
which is why the more appropriate version is probably $\det A=\exp(\operatorname{tr}\ln A)$
 
Astyx
Astyx
Wait, is exp injective ?
 
copper.hat
copper.hat
If it is diagoalisable then no surprises
 
Fargle
Fargle
9:44 PM
It isn't injective IIRC
 
Semiclassical
Semiclassical
or $\det e^{B}=\exp(\operatorname{tr} B)$
 
Fargle
Fargle
So what I said is a bit goofy but it can be twiddled to be less goofy
 
Astyx
Astyx
I think you define the log for matrices with the series expansion of $\log(1+x)$
 
Fargle
Fargle
Oh, that makes more sense
 
copper.hat
copper.hat
what is the underlying space you are talking about?
 
Fargle
Fargle
9:46 PM
Forgive me, it's only 3:45 PM, too early for my brain to work
 
copper.hat
copper.hat
mid west people
my backup has 7 mins remaining for the last 10 mins...
always wonder about arithmetic in microsoft land
 
Astyx
Astyx
Maybe your computer is moving very very fast
 
copper.hat
copper.hat
it doesn't have a hangover...
hate glancing over my old functional analysis notes and realising how little i remember...
 
user2103480
user2103480
@Astyx Let it be given that $T \in L(H)$ is nonnegative, symmetric and of finite trace, so that a basis $(e_k)$ of eigenvectors with eigenvalues $\lambda_k$ exists. Then $$\mathrm{tr} \log(1 - T) = \sum_k \langle \left( \sum_n \frac{(-1)^{n+1}}{n}T^n\right)e_k,e_k \rangle = \sum_k \sum_n \frac{(-1)^{n+1}}{n}\lambda^n$$
and for appropriate eigenvalues this gives us the logarithms
that's why the constant epsilon is up there above
 
copper.hat
copper.hat
missing a $k$ presumably...
 
user2103480
user2103480
9:59 PM
ah yeah it should be $\lambda_k^n$
 
Astyx
Astyx
Right yeah
It all comes down to eigenvectors of A being eigenvectors of $\log 1+A$
 
Semiclassical
Semiclassical
this question bounty sorta irritates me: math.stackexchange.com/questions/3982493/…
 
user2103480
user2103480
What's the power series of x^s again
 
Semiclassical
Semiclassical
"Oh, no one has answered it yet, better bounty it" "No one has answered it yet because you ask why X is the answer to a question you don't ask"
@user2103480 about what x? if x=0 there's no power series to give
around x=1 it's the binomial series
 
Astyx
Astyx
$(1+x)^s = 1+sx + s(s-1)x^2/2 +\dots$
if that's what you're asking
 
user2103480
user2103480
10:15 PM
that probably suffices. I'm looking to define the fractional laplacian with the power series so it'd be something like $(-\Delta)^s = I -s(\Delta + I)) + s(s-1)(\Delta + I)^2/2 + ...$
going all heaviside there
 
Astyx
Astyx
That should work I think
 
user2103480
user2103480
That should make it easier to show hilbert-schmiddity
 
polite proofs
polite proofs
Let $A$ be a nonempty set and let $B$ be a subset of the powerset $\mathcal{P}(A)$ of $A$. Define a relation $R$ from $A$ to $B$ by $x R Y$ if $x \in Y$. Find two such sets $A,B$ and $R$ for these sets.

The solution says that $A = \{a,b,c\}, B = \{\{a\},\{a,b\}\}.$ Then $R = \{ (a,\{a\}),(a,\{a,b\}),(b,\{a,b\}) \}$

But isn't this invalid? $a$ is not an element of $B$
 
Astyx
Astyx
$(k^2)^s = \sum_n {s\choose n}(k^2-1)^n $
 
user2103480
user2103480
you calculating the fourier stuff?
 
BigSocks
BigSocks
10:19 PM
where is it implying $a \in B$?
 
polite proofs
polite proofs
"Define a relation R from A to B by xRY if x∈Y."
 
Astyx
Astyx
Yeah, I find it much clearer to think of $-\Delta$ as $k^2$
 
polite proofs
polite proofs
x in Y, so in this case, if R has (a,{a}), then a is in B
 
BigSocks
BigSocks
nah, that says $a \in \{ a \}$
looks good to me
 
polite proofs
polite proofs
How?
Which part says that $a \in \{a\}?$
 
BigSocks
BigSocks
10:21 PM
first element of the relation
 
polite proofs
polite proofs
OH! Never mind
I was misreading it, wow!
Thanks
 
Semiclassical
Semiclassical
aR{a} if a in {a}
 
BigSocks
BigSocks
np
 
polite proofs
polite proofs
Yes, right.
 
Semiclassical
Semiclassical
Which means R is effectively just $\in$
 
 
1 hour later…
Ted Shifrin
Ted Shifrin
11:23 PM
I wonder how many of our chat denizens should be named impolite proofs :D
 
user2103480
user2103480
I'd rather go by impolite heuristics
 
Ted Shifrin
Ted Shifrin
Are you prone to heuristics?
 
user2103480
user2103480
I didn't have mandatory exercise sheets in a math subject in a year, so I mostly don't write down a lot of details for time reasons
 
Ted Shifrin
Ted Shifrin
Ah. Feedback on written work is important.
 
user2103480
user2103480
it is, but time consuming for both sides. Even more so with everything online
 
Ted Shifrin
Ted Shifrin
11:29 PM
Agreed. I think one of the most worthwhile things I did in my 38 years of teaching was to grade homework and write lots of comments. (Not in elementary courses, but in upper-level and graduate courses.) Most university faculty didn't do such things.
 
BigSocks
BigSocks
why do you think so?
 
Ted Shifrin
Ted Shifrin
Because (a) I knew what my students got and what they didn't get; (b) specific feedback on both mathematics and exposition improved their knowledge and communication skills. Many of the students did ultimately thank me for it.
 
user2103480
user2103480
Ah. When I graded homework, I also wrote down a lot of comments. Many math people are too discouraging. I liked to explain at what point people went wrong or how one could fix the argument
 
Ted Shifrin
Ted Shifrin
It's different reading ten of the same misimpression and commenting on it, and knowing I have to discuss the issue in class, as opposed to a grader maybe catching it or maybe not, maybe telling me or more likely not.
 
user2103480
user2103480
Sometimes, people - even in math for biologists classes - had good ideas but not the right tools, and I didn't like just subtracting points
 
Ted Shifrin
Ted Shifrin
11:32 PM
Yes, I still remember the grad student who graded when I took Guillemin & Pollack Differential Topology as an undergrad. He was highly condescending. In hindsight, his comments were nevertheless correct, but still the tone sucked. But I always told my students this story.
I think it's better to grade homework with more discipline. Otherwise they think they're doing it right and then lose major points on exams and are rightfully pissed off.
Of course, if they didn't learn from my comments and still did it wrong, that's their fault, not mine.
 
user2103480
user2103480
Yeah the common or "interesting" mistakes I always explained to everyone when giving back the sheets, ofc without actually making any comment on who did the mistake
 
Ted Shifrin
Ted Shifrin
Yes, of course.
But occasionally I praised students for outstanding or creative things. I had a few students who got very embarrassed when I praised them, so I learned not to.
 
Thorgott
Thorgott
are proofs by sledgehammer impolite
 
user2103480
user2103480
@TedShifrin yeah it's important to know the exam standards
 
Ted Shifrin
Ted Shifrin
No, proofs by arrows are, @Thor.
 
user2103480
user2103480
11:35 PM
@TedShifrin I'd only praise anonymously, saying that such and such is a good solution I saw. The actual praise was written in the comments on the sheet
 
Ted Shifrin
Ted Shifrin
Did you sort out my Euler class comments yet, @Thor, or shall we save that for another week?
I had one student whose solution to a challenge problem in the first problem set was far better than what I had proposed in the hint to the problem in the (published) textbook. She was afraid she was wrong. I ultimately changed the problem in the next published version and credited her in the preface. :)
 
user2103480
user2103480
nice!
 
BigSocks
BigSocks
hmm that's pretty cool
 
Ted Shifrin
Ted Shifrin
I also had a student in linear algebra years and years ago who suggested a much better proof (for why the usual row reduction procedure produces a two-sided inverse) than most textbooks have. I used his proof in my books and thanked him, too.
I can't believe I hadn't read it in books before that.
 
user2103480
user2103480
ah, I miss the first semester, where I was told my solutions were better than the profs. Now I'm proud to even have a good guess at a problem
 
Ted Shifrin
Ted Shifrin
11:37 PM
LOL ... yes, that's the price of progress, @user2103480
 
Thorgott
Thorgott
we'll save that for when I know complex bundles
 
Ted Shifrin
Ted Shifrin
You can understand the negative if you buy that a meromorphic vector field counts the usual Euler characteristic. That's just Poincaré-Hopf without mentioning bundles.
 
user2103480
user2103480
I did two courses on computer linguistics
 
Ted Shifrin
Ted Shifrin
LOL
 
user2103480
user2103480
The general linguistics were very interesting, the statistical methods extremely boring and ad hoc
Now I'm just waiting for linguistic topology to happen
and will never touch statistical natural language processing again
the grammar/logical part of NLP is probably even worse
neural nets and SVM are pretty good with the "local properties" of language, like translating sentences, so I'd really hope there's some geometry behind that
or TOPOS, as @BalarkaSen likes to call it
 
Thorgott
Thorgott
11:51 PM
I can't even tell what the right notion of meromorphic vector field is
 
Alessandro Codenotti
Alessandro Codenotti
@TedShifrin What about impolite profs?
 
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