Mathematics - 2023-04-24 (page 1 of 2)

one potato two potato

00:31

I hate summer. Especially I hate heat.

robjohn

01:06

We're in it now.

Ted Shifrin

checks calendar for April

one potato two potato

So my motivation for meromorphic function on (compact) Riemann surfaces is that a single nonconstant meromorphic function completely determines the complex structure of the given RS, i.e. we can write the local coordinate in terms of a single meromorphic function. Is there any other importance? or are people just wondering how many meromorphic function can be?

robjohn

@TedShifrin the heat, not the summer

Ted Shifrin

Well, you don’t get very far studying holomorphic functions, so what do you suggest?

@robjohn Ah.

Ted Shifrin

02:16

@onepotatotwopotato P.S. Remember that mero fns on $X$ are holo maps $X\to\Bbb P^1$.

AMDG

04:12

Freezing cold > steaming heat unless you mean a sauna

Gwyn

09:19

Is proving that $a_n \to \infty$ (that is, $a_n$ is in a neighbourhood of $(-\infty,-m) \cup (m,+\infty)$ for some $m>0$) equivalent to proving that $|a_n| \to +\infty$?

I think yes, because $(|a_n|>K) \iff [(a_n>K) \lor (a_n<-K)]$ and $[P \implies (Q \lor R)]\iff [(P \implies Q) \lor (P \implies R)]$

ephe

Can anyone think of a very simple partial order relation on natural numbers such that there are no maximal or minimal elements? My professor gave an example about this last term but I can't remember.

QuitMSE

a~b iff a\le b ( natural/usual ordering)

fantasie

09:37

Hello! In harmonic analysis, there is a notation $\tilde \phi$. Particularly, in this context: let $u$ be a Schwarz function and $h$ a tempered distribution. Define the convolution $hu$ by $<hu,f>=<u,\tilde h*f>$. I wonder what this tilde stands for.

ephe

@QuitMSE but then isnt 0 a minimal element?

QuitMSE

If 0 is natural number then yes, otherwise 1 is the minimal element but it doesn't have any maximal element.

fantasie

@ephe You can make a bijection f between all integers and positive numbers and use the induced order. Alternatively, make an order s.t. odd numbers < 0 < even numbers, say ... <3 < 1 < 0 < 2 < 4 < ...

Soumik Mukherjee

yesterday, by Soumik Mukherjee

Let $X=Y=$ the line joining $(0,0)$ and $(1,0)$ $\cup$ the line joining $(1,0)$ and $(1,1)$ . Now in $S=[0,1]×[0,1]$ let the line joining $(0,1/2)$ and $(1,1/2)$ gets mapped to $X×(1,0)$. Then the upper side of $S$ gets mapped to $X×$the line joining $(0,0)$ and $(1,0)$ and the lower side of $S$ gets mapped to $X×$the line joining $(1,0)$ and $(1,1)$

@TedShifrin Professor, can you please tell if this is a valid counter example to @eternalfool's generalization?

fantasie

Hello! In harmonic analysis, there is a notation $\tilde \phi$. Particularly, in this context: let $u$ be a Schwarz function and $h$ a tempered distribution. Define the convolution $h\ast u$ by $\langle h\ast u,f\rangle=\langle u,\tilde h\ast f\rangle$. I wonder what this tilde stands for.

robjohn

10:32

@fantasie see Hermitian Adjoint

ephe

10:43

@fantasie Thank you!

If f and g are functions both from the finite set X to again X, and gof is injective, why should g also be injective? I can't see why X being finite changes anything.

robjohn

11:04

On a finite set, an injective map is surjective and a surjective map is injective. If $g\circ f$ is injective, it is surjective and so $g$ is surjective and therefore, injective.

ephe

@robjohn Oh okay thank you!

robjohn

11:30

Consider functions on the non-negative integers. Let $g(k)=k-1$ for $k\ge1$ and $g(0)=0$, g is not injective since $g(0)=g(1)$. Let $f(k)=k+1$. However, $g\circ f(k)=k$ is injective.

Ajay

12:57

Just so you guys know there is a user with an anime girl(blue color) as their profile posting ongoing olympiad problems

Here is one such question

They have deleted the post now.

But I suspect they'll be back. They always come back...

user 858770

13:24

Xander Henderson

@Ajay If they are posting problems which are (a) publicly viewable, and (b) posted in violation of some publicly viewable policy, please flag them. We do have a policy against cheating in competitions.

geocalc33

13:38

0

Q: $\xi(s)=\xi(1-s)$ functional equation from $\Gamma(s)\Gamma(s+1)\zeta(s)=\int_0^\infty t^{s-1}\sum_{\alpha \in \Bbb N} \Phi_{\alpha}(t)~ dt$

The following came up for me while doing an exercise in geometry. I considered a smooth foliation $\Phi_{\alpha}(t)=2\sqrt{\alpha t}K_1(2\sqrt{\alpha t})$ of the manifold $(0,\infty)\times (0,1).$ I then invoked the following relationship between $\Phi_{\alpha}(t)$ and $\zeta(s),$ the Riemann zet...

I'm wondering to how to derive the $\xi(s)=\xi(1-s)$ functional equation for a particular integral involving the gamma function and zeta function

fantasie

@robjohn Thank you!

geocalc33

$\xi(s):= \pi^{-s/2}\Gamma(s/2)\zeta(s) $

one potato two potato

The algebra professor I talked about before said that he doesn't believe exams as a way to evaluate students. So whenever he needs to make a choice between interesting problems and good problems to evaluate students, he sets interesting problems as exam questions (which usually makes his exam questions hard to solve in a given limited time). He wants students to think about exam questions after the midterm.

Xander Henderson

@onepotatotwopotato I have sympathy for that point of view.

shintuku

13:55

bad professor, his class doesn't exist in a vacuum and students need to aim for grades to have a chance at making their degrees useful

one potato two potato

Registering Algebra 2

Xander Henderson

@shintuku I don't see where @onepotatotwopotato indicated that hard questions are equal to bad grades.

shintuku

he makes a chocie between interesting problems and good problems

Xander Henderson

@shintuku Yes, and?

shintuku

which usually makes his exam questions hard

Xander Henderson

13:59

@shintuku Yes, and?

shintuku

infer, xander, infer!

Xander Henderson

Again, hard questions does not mean the same as hard grades.

@shintuku I think that you are over inferring.

shintuku

why would you think that

Xander Henderson

@shintuku Why do you think that hard questions should imply low grades?

shintuku

logically imply, i wouldn't know

but correlate

Xander Henderson

14:01

@shintuku I really don't understand your point.

I can give an exam with a lot of very hard questions and still give As.

shintuku

yeah but are they good questions?

Xander Henderson

@shintuku You are moving the goal posts.

You said it was about grades.

shintuku

it is!

Xander Henderson

@shintuku Then please connect the dots for me an explain exactly what your point is.

Because I don't understand.

shintuku

well, are you giving out A's because you like students, even if you give difficult answers?

Xander Henderson

14:03

The idea of giving interesting problems that students think about after the exam is exactly what learning is supposed to be about. So, pedagogically, it seems like good practice. And your objection is that student's grades will be lower, but I don't see why that has to be so.

shintuku

i wouldn't understand how you don't understand

Xander Henderson

@shintuku What?

shintuku

there! there it is!

that's the vacuum classroom thinking

Xander Henderson

On an exam, you get a score (computed in some manner). You then translate the aggregate scores from whatever assignments you give in a class into a letter grade.

shintuku

of course, if it helps learn, great

but you're prioritizing learning over grades

that makes no sense at all

Xander Henderson

14:04

@shintuku I really don't understand what your objection is.

shintuku

it would make sense if learning was a primary objective, but it isn't, it is secondary. of course, realizing the goal of learning also helps and obviously comes with positives and desirable outcomes

but then, beginning to focus on learning to the detriment of the actual conditions the students find themselves in, is harmful

Xander Henderson

@shintuku Your objection seems to be that if real learning is taking place, then students aren't getting good grades.

You are wrong.

shintuku

that's a strawman!

i have said no such thing

you are over inferring here!

Xander Henderson

You have refused to explain your position, hence I have no choice but to rebut what you seem to be saying.

shintuku

learning is great

Xander Henderson

14:06

I have repeatedly asked you to clarify, and you refuse.

shintuku

well, that is over inferring, xander

and you are jumping to the conclusion i refuse to clarify, that is also over inferring

user4539917

Ok, ok. Let's time out please 🙏

shintuku

i think learning is great

and it is a great outcome to aim for

that being said, it is a secondary objective, considering the structure and the worth of grades in the education system, the way it is organized

and especially! in academia

Xander Henderson

@shintuku Strong disagree.

anak

@XanderHenderson Do you mean here "...is an example of what learning is supposed to be about", rather than "...is exactly what..."?

shintuku

14:09

the proper place to recall this notion of learning is in school boards, at the state level, and in other organized committees that decide what type of learning will be undergone in classrooms

there, this ideal of learning above all is great

user4539917

In this day and age of JEE suicide rates going up, we need to be open minded.

shintuku

and it needs to come with concrete plans on how to make it a reality and realizable

Xander Henderson

@shintuku School boards? For colleges and universities?

What are you talking about?

shintuku

now now xander you need to be charitable here, obviously i think also of the relevant authorities in the universities which decide of the relevant program requirements

and also, france has a unified board that discusses these issues at the national level

even for colleges

Xander Henderson

Those bodies don't exist in the US.

We have something called "academic freedom".

Franklin

14:12

shintuku

which is worse!! how can you not see how that makes it even worse? imagine having to adapt university programs purely on the needs of the markets?

Xander Henderson

We believe that the highly qualified people who we have hired to conduct research and provide instruction are, you know, highly qualified people, and that they should have the freedom to do their jobs.

shintuku

you will find it considerably worse time making things about learning when you need to adapt to the private needs of the market, both in terms of getting students to study in your university and get them to be qualified enough to get hired on the basis on their degree

Franklin

I think something's wrong with the calculation of the 3rd derivative, isn't it?

shintuku

in other words, learning is secondary, even worse, in the face of extremely localized decision-making authorities who need to first of all focus on the economics, and only second about learning

especially when the interests of the administrative authorities of the private university comes before any other possible interest

isn't grade inflation a thing?

trying to make students "learn" things when getting a bad grade could mean not having access to certain graduate programs or job opportunities in insane!

it's not at the level of classroom we need to focus on to make this reality of learning real. it's at the levels of whichever organizational authorities decide what has to be given in the classrooms

spare the students the learning, please!

anak

14:18

Having been responsible for the learning and assigning of grades in a university math course, I don't think I ever once considered the economics during my course, @shintuku

Xander Henderson

@shintuku Wait... I'm confused... you are complaining about grade inflation here...

@shintuku ...yet complaining about low grades here.

You seem to be contradicting yourself.

Also, again, you assuming that hard exams equate to low grades. Why make that assumption?

shintuku

don't nitpick, the overall argument sustains itself. grade inflation is meant to point out the fact that grades do have disproportionate importance with respect to learning, and low grades is a problem because it will ruin you, even if you are doing learning

@anak right, but certain authorities constrain these choices, and these authorities have as their primary interest the sustainability of the university

anak

@shintuku Constrain them how exactly?

Xander Henderson

You have yet to provide any evidence that hard exams correlate to low grades. Your entire argument seems to be built on this specious assumption of correlation. Until you can explain why you believe that this correlation exists, there is really nothing else to say.

shintuku

@anak examples at the level, of for example, philosophy departments, is the disproportionate emphasis and requirement of analytic philosophy in US universities as opposed to, for example, continental philosophy

Franklin

14:22

Ah, I am sorry! The thing seems alright. Thank you!

anak

@shintuku You mean they hire more analytic philosophers than continental ones? I don't think that's different across the ocean.

shintuku

@XanderHenderson that's not the point of the argument...

and there's no contradiction, give the appropriate charitable work and interpretation

@anak it's at least not as disproportionate!

anak

@shintuku How are you making this claim? Do you have data that you are looking at to make this deduction?

shintuku

with respect to the stamping out of Hegel and pragmatists in the philosophy departments, there is at least an argument to be made

two seconds, i have a reference somewhere

my aim is not to establish these propositions as undubitable truths, but to at the bare least make the idea of "learning" as primary in university instutitions as dubitable

i.e., i can't convince you, but I do believe I have enough to make it a viable, legitimate path of argumentation, and put the opposite stance on unstable footings

let me get that hegel reference for you 2 secs

anak

Well the context of this was discussion began as a math classroom, and now the examples are leaving that area into philosophy departments, so I am looking to ground these statements as "probably true" as it's quickly leaving the area of relevance to me.

shintuku

14:30

the basis for the argumentation for the math classroom part comes from a series of phenomenological observations, not on the same basis as what happens for philosophy, but by analogy i think there's a similar phenomenon

have you ever seen how engineering students disdain proper mathematics?

anak

Sorry, what is "proper" mathematics?

shintuku

proof-based mathematics, theorem-based mathematics, non-computational

anak

Oh, you mean mathematics that isn't really useful to them, sure.

Yes, I've noticed that students prefer topics closer to their interests. What about this phenomenon?

shintuku

hegel reference: time in the ditch, american philosophy and the mccarthy era

@anak i wouldn't look anywhere else than engineering students to see the disproportionate importances of grades wrt. mathematics

they are the ideal example, but the same phenomenon is clearly visible to anyone else studying even in something they enjoy

i recall this anecdote about this insanely difficult harvard freshman class on algebra or analysis, i don't recall, honours maybe, where a small percentage of students passed, and among those, an important percentage confessed not to understand the material

anak

@shintuku engineering students not caring for proof-based mathematics is evidence of the disproportionate importance of grades?

Can you unpack that a little bit more for me? I don't quite follow.

shintuku

14:38

again, i'm not trying to establish this as an absolute fact and only the relativity of the opposite view, and i'm supposing charitable attempts at interpretation so i don't have to spell everything out

can't you find some reasons why that would be the case?

i mean, the relationship between learning and grades, in engineering students that have to take mathematics

if I take a mathematics class, i'm interested in learning all theorems that justify my calculations

an engineering student will tend to view things with respect to their applicability, and whatever, i'm not a psychologist

the point is that the engineering students are the extreme case of the possible dissonance between grades and learning in mathematics

anak

@shintuku Are you suggesting that engineering students should feel the same way (as you)?

shintuku

no anak, i'm not

they're an ideal case example of dissonance between grades and learning

with respect to mathematics, i.e., they can serve as the starting point of interpretation to find where else the phenomenon appears in lesser degrees

fantasie

@shintuku I can back on this statement: back in collage I talked to many students in chemistry and physics, and this is their attitude towards mathematics

anak

@shintuku Sorry, I really am not following. You keep on suggesting that engineering students are some extreme case of dissonance/disproportionality, but the only (partially) explicit description of what engineering students actually do is given here, and I don't see an issue with them doing this (and hence I don't see where the dissonance/disproportion is occurring). Can you elaborate on this part at all?

shintuku

sorry i'm getting a bit bored here, i feel the general argument is more or less clear and i'm not that interested in writing it out in essay format

anak

14:47

It's anything but clear to me. But sure, feel free to not elaborate if it's too tasking.

Xander Henderson

@shintuku I mean, both of your interlocutors have expressed confusion about what your point is. So I don't think that you are being clear.

shintuku

cheers, we can continue some other time

i hopefully at least have brought some interesting talking points for future conversations

Astyx

The point about proper mathematics being non-computational is certainly ... interesting

shintuku

notice that it was one of the things, not the only thing i said about proper mathematics. i need a bit of charitable interpreting here

anak

Charitable interpretation usually requires us to understand a significant chunk of what you are saying. In my case at least, I couldn't.

2

shintuku

14:58

it's not that you can't, you understand well, but you disagree. those are distinct things

Xander Henderson

@shintuku Please don't call other people liars.

shintuku

it's not that you can't understand how the different points of the argument are related, it's that you disagree that they're related prima facie

i'm not calling anyone a liar, again why do you read me as some sort of opponent

it's frankly boring to be read as somehow disingenuous

this is your basic stance in this entire conversation, how are we supposed to have friendly bantering?

anak

Sorry, did you say that (despite me saying I could not understand a significant chunk of what you are saying) that I actually understand you well?

Xander Henderson

@shintuku You said "it's not that you can't, you understand well, but you disagree. those are distinct things", which explicitly calls someone a liar.

shintuku

no, you're supposing that because you're intent on reading me as somehow disingenuous. frankly, very boring conversation

Xander Henderson

15:02

@shintuku Maybe you didn't mean to imply that others are lying, but that is precisely what you said.

Do you want to double down on that, or maybe apologize?

fantasie

It's not worth apologizing. It is a very, very boring that needs a termination.

shintuku

i apologize if I'm offending anyone, but in the future i will keep in mind this is how you converse. very boring conversation, very boring to be read so disingenuously

very boring to suppose I somehow am out to offend you

geocalc33

I just came across the concept of surface interpolation

I need to smoothly interpolate through four space curves

it's like interpolating the factorial function with gamma but with surface

geocalc33

15:19

but my primary objective is not that. It's to find a Cauchy foliation of $\Bbb R^{3,1}$ in null coordinates

If anyone knows of a resource that defines of such let me know.

I do know that the metric will be: $g'=dudv-dw^2-dr^2$

shintuku

16:02

@anak so, i've recharged a bit and am up for some more conversation. if you have time, i'm up for discussion if you're up for discussion. you were saying, you don't understand how the behaviour of engineering students suggests a dissonance between grades and learning?

anak

Sure.

shintuku

do you think someone can pass a class without understanding it? or can get good grades without learning?

anak

Not super comfortable with how ambiguous of what "understanding" or "learning" is there, but sure, I've seen plenty of serious academic integrity cases.

shintuku

in your opinion, what motivates a serious academic integrity case?

anak

I don't think there is any single motivation. Students cheat for a number of reasons, and it's almost always a mixture of reasons.

shintuku

16:11

could you name some of them?

anak

Someone had mentioned suicides related to JEE earlier. Mental health and societal, familial, and economic pressures seem to be relatively common.

shintuku

I also agree with your suggested motivations. Have you heard engineer graduates, or heard of such graduates, suggest that university doesn't matter, the important part of the field for getting a good carreer in engineering is where you get experience at?

anak

No, I have not personally heard that opinion.

shintuku

Have you heard it maybe of computer science graduates, computer science-field workers with no university degree?

anak

No, I haven't heard anyone with a university degree suggest that university doesn't matter.

And I don't really know any people in CS without a university degree. Maybe only IT and being >50 years of age.

shintuku

16:18

When you say "suggest that university doesn't matter", do you think that sentence has a unique interpretation, maybe among the lines of: "it is better not to go to university at all", or in your interpretation, can there be degrees of importance one attributes to university?

for example, in a spectrum going from, "you can skip it and your life won't change" to, "it completely determines your future possibilities"

anak

Well let me steelman what I think you are going for. I know of graduates who have the experience that they got more out of their co-op program than out of the classes they took. Does that help move us forward to getting out of anecdotes and into the actual argument?

Obliv

does this have an elementary antiderivative $2xye^{x^2y}$

w.r.t. x

anak

@Obliv yes

shintuku

@anak in what sense do you think they have gotten more out of their co-op programs?

relatively to classes they took?

Obliv

$2y\int xe^{x^2y}dx$ but if I do by parts doesn't it just get more complicated

oh wait nvm

anak

16:24

@shintuku They enjoyed getting to apply the theory they learned from their classes in a setting that interests them. This degree of application was absent from their classroom.

Obliv

um wait nvm nvm, I don't see it. I put it into wolfram and nothing came out

shintuku

@anak in other words, to you, they are simply expressing that they have enjoyed their co-op more, and have not enjoyed their classes that much. Would this be a correct assessment of your understanding?

anak

@Obliv wolframalpha.com/input?i=%5Cint+2xye%5E%7Bx%5E2y%7D+dx

Obliv

ooh I accidentally put $(xe)^{x^2y}$

anak

@shintuku That they enjoyed their co-op program more than their classes.

Ajay

16:26

@XanderHenderson Yeah sorry

They deleted the question before I could.

They claimed it was from an old trivia contest in their school. When I asked for a link, they deleted the post. I guess that is evidence enough.

shintuku

@anak in the case of a hypothetical engineer that said: "i've learned more from experience on the job than from my time in university", would you suggest he is expressing that he has enjoyed his time on the job more than his time in university?

Obliv

this might sound silly but what is the operator on the u-sub so that we have $u \to du$ and $f(x,y) \to F_x dx$

anak

@shintuku I don't know. I don't know if that statement necessarily has anything to do with enjoyment.

shintuku

@anak I understand, have you heard of this statement previously, from anyone? Furthermore, are you able to understand this statement?

anak

@shintuku I can't pinpoint an exact situation where this has occurred to me. Are you able to express your position without appealing to anecdotes?

shintuku

16:33

I am currently verifying whether you understand the terms of the conversation, which you have suggested you don't. In identifying the points you don't understand, I will be able to adequately correct the points of misunderstanding, if there are any legitimate such points of misunderstanding.

Ted Shifrin

@Obliv It doesn't sound silly. It makes no sense at all.

shintuku

If you cannot pinpoint a situation where this has occured to you, can you confirm whether such a situation has occured to you, or has been heard by you, even if you can't pinpoint with exactitude when?

anak

@shintuku I don't think this hypothetical engineer's statement is controversial. Most professions would probably agree that a 4 year degree preparing you for job J eventually is dwarfed by years of experience working in job J.

Obliv

@TedShifrin We didn't really cover the extension of the u-sub technique in integration to multivariable calculus so I'm wondering what it is in general for more than a single variable

Ted Shifrin

There is an important thing called the change of variables theorem. An example is converting a cartesian integral to polar coordinates. It is much more complicated than the single-variable situation.

Obliv

16:36

Oh.. I see it in my book it's one of the sections we skipped or glossed over I guess

Change of variables: Jacobians

I'll look over it thank you

shintuku

@anak In a case where someone suggests, as you said, that years of experience dwarf time spent on a degree preparing you for a job, which do you think, for them, correlates more strongly with job performance, their grades or their years of experience?

anak

Their experience.

Since they said they learned more through that...

Obliv

@TedShifrin I know your feelings on Spivak's manifolds, what about his early transcendental functions book? I noticed I had a spare copy from years ago and I like physical copies of textbooks. It's different from larson for sure. I'm not sure which I like more

I think larson is less verbose which I like

shintuku

I would also agree. In order to obtain a job coming out of university, which one do you think correlates more strongly to achieving said job? Degree of learning and understanding, or grade performance? @anak

Ted Shifrin

I don't know what you're talking about. He didn't write a standard calculus textbook ... so "early transcendentals" is a complete no-go.

Obliv

16:41

Oh I mixed him up with stewart.

Ted Shifrin

Uh huh.

Obliv

Spivak stewart, tomato tangerine

anak

@shintuku I don't think that's uniform even within a discipline. Those things are entirely determined on an employer-by-employer basis.

shintuku

Would you agree with the statement: better jobs are available coming out university if you have better grades?

Be it, academic or otherwise?

anak

No. That statement is contingent on a lot of things.

shintuku

16:45

I understand. Which things do you think the statement is contingent upon?

Can you name a few?

anak

the employer is kind of the key thing

Do you think that the statement is agreeable?

shintuku

I do! I would go as far as to say, job opportunities are strongly correlated to academic performance

Positively: job quality AND availability correlates with academic performance

just to be clear, we disagree on this?

anak

I'm currently struggling to find an anecdote in my experience where an employer asked to see someone's transcript, beyond candidates for a graduate program.

shintuku

So, would you agree this is true at least for academia?

anak

In math? Probably not at all.

shintuku

16:52

Would it be an accurate representation of your views that, this seems true in most academic programs, but not in mathematics?

anak

Sorry, what do you mean by "academic programs"?

shintuku

Graduate degrees for physics, philosophy, chemistry, etc.

Masters and onwards

anak

I don't have experience applying to these programs so I don't know their application processes.

shintuku

In other words, you do not think this is true of academia, because you only have experience of mathematics, and do not consider it to be true in mathematics.

anak

But I was responding for jobs in academia, not applications to degrees.

shintuku

16:54

Oh, I understand now, sorry for misinterpreting

Teaching positions, that is?

anak

Professor and post-doc positions.

shintuku

But however, that is not true in mathematics, if I understand you correctly.

anak

I don't think they ask for transcripts for these positions.

shintuku

In other words, there is no job whose quality and availability correlates strongly with GPA. Not in academia for mathematics, from your personal experience, and not academia in other academic disciplines, or at least, you don't know if it would be true in those cases.

Would this be an adequate representation of your views?

anak

No.

Also, recall that this discussion was me asking for more information on your position.

To this point you still have yet to elaborate on what you were saying earlier.

Obliv

17:00

Aren't the ones with the most money in the world those that didn't go through the academic mill and went off and did their own thing?

If we consider their wealth as their proportion of "success" then those few anecdotes dwarf the millions with stable and good jobs

anak

@Obliv Usually they are ones who could afford (often through other means) to avoid having to go through school.

e.g. parents were able to fund business ventures.

shintuku

@anak Then, by negation, there is at least one job whose quality and availability correlates strongly with GPA?

anak

@shintuku No. That's not how a negation works when you load it up with "and"s.

Please feel free to respond to this in the meantime: chat.stackexchange.com/transcript/message/63439181#63439181

shintuku

I'm sorry, I'm simply trying to figure out how you don't understand what I'm saying, and I think I'm getting close

It seems to me you're in obvious contradiction to yourself

anak

I think it's more efficient for the both of us if you simply explain what I didn't understand further.

Instead of playing this "i'm going to diagnose what's wrong with you!" game.

Obliv

17:06

What is the point of this conversation

shintuku

I have considered that line of argumentation a less able statement of my opinions, and consider the current line of questioning a more adequate way to further my argument

I currently see that you both agree and disagree about correlation between GPA and job availability and quality.

I'm thinking maybe your ability to give a charitable interpretation is failing due to your ability to sustain a coherent viewpoint about what it would be to understand the argument

anak

@Obliv since you showed up? I haven't the foggiest. Before shintuku was going off on someone while making vague statements. When asked to clarify he refused. This is currently Episode II.

@shintuku are you going to elaborate on the point I asked you to, or are you going to pretend that you making claims about my beliefs somehow solves the original problem of no one understanding what you were saying before?

shintuku

I'm sorry, but I consider GPA to strongly correlate to job opportunity and quality, and consider this an adequate representation of my views. You both do and don't.

I'm sorry, I believe you don't understand the previous point because you do not have a coherent, non-self-contradictory understanding of the meaning of the argument.

Until you can resolve this, I deem this conversation bound to fail, due to your inability to propose a coherent understanding of the subject at hand

But feel free to tag me if you can resolve that issue.

anak

I am surprised it took this long to uncover that you were just going to default to engaging dishonestly.

Cheers.

shintuku

I'm sorry, there is only so much I can do, and I've repeatedly given you the chance to correct your views, and you haven't. For some reasons, you don't think I can correct them in the same way, and refuse to take my word when I say I am adequately representing them at this moment. I would consider that dishonest, instead.

Cheers.

geocalc33

17:13

5

Q: What is the metric for this product manifold?

Consider a spacetime $(\zeta^{3,1},g)$ where $$g=\frac{dudv}{uv}-\frac{dr^2}{r^2}-\frac{dw^2}{w^2} \quad \forall u,v,w,r \in (0,1)$$ Now this is just Minkowski space in different coordinates (related to Dirac/Light cone coordinates/null coordinates). I'm looking to take a Cauchy foliation of $\ze...

differential-geometry manifolds physics mathematical-physics semi-riemannian-geometry

As you can see I've really emptied my toolbox here

Also put a bounty on it

No answer to date though.

I think there are some gaps in the argument that need to be filled in in order to get an answer

anak

Maybe math.overflow might be a place you could share it? Though I think you might have to give research relevance to it in order for it to be on-topic.

Devang Tripathi

If a variable point P in space moves such that
PA2 – PB2 = a constant, where A and B are 2 fixed points, then prove that the locus of P is a plane. can someone help here in visualisation?!

Xander Henderson

University degrees are not job training. The fact that many employers seek out people with degrees (and, perhaps, high grades) is an indication that they, as employers, value what the academy offers to students. This does not imply that universities should give a rat's tuchus about what employers want. It seems that if employers want what universities have to offer, then maybe those universities should not change their practices in an attempt to please these employers.

geocalc33

Yeah I'm hesitant to share it on mathoverflow just because I haven't been able to connect it strongly to research but if I can find some more motivation I probably will try sharing on MO

Ted Shifrin

@DevangTripathi I don't understand your notation. You need to do better than pasting in typing.

Are you saying $\|PA\|^2 - \|PB\|^2$ is constant?

Xander Henderson

17:18

But, let us say for the sake of argument that I should care about how the grade I give a student will effect their employment prospects. How in the heck does this relate to the original comment which started this conversation, e.g. that I am sympathetic to an instructor who prefers to give interesting problems on exams?

fantasie

@Obliv I believe this conversation start with a debate on should professors give their students interesting but hard mid-terms, and then move on to if GPA correlate to ones job opportunities, and moved on to how does "engineering student will tend to view things with respect to their applicability" interacts with points made before, with a minor deviation about etiquette and manner, and somehow moved back. Probably still takes takes weeks if the original problem would be ever resolved.

Ted Shifrin

@DevangTripathi The plane is the perpendicular bisector of the segment joining $A$ and $B$.

Soumik Mukherjee

@TedShifrin I earlier tagged to an answer in the chat, can you kindly have a look if you have the time?

Ted Shifrin

I haven't thought about what you said, @Soumik. Sorry.

You should tag the person who suggested the generalization in the first place :)

Miss Mae

@XanderHenderson piggy-backing on this, the the public university I work for changed their policies and such after a rather large donation by a national bank, in that they’re changing a classroom to have the “First National” logo in the room on all the equipment as the bank is funding it all, and dictating how the educational space will be used. Previous policies prevented logos of non-university parties being displayed in classrooms, but after one meeting and that donation the policy changed

Soumik Mukherjee

17:24

@TedShifrin Okk, actually I wrote that intuitively, i didn't tagged that person because I wasn't totally sure if my answer was correct

Miss Mae

a lot of these changes usually come from random donations after closed meetings, but nonetheless it’s icky when corporations are trying to dictate what colleges should teach and such - there should be a hard line/separation with corperations and education

Xander Henderson

@MissMae Yikes. That's gross.

Ted Shifrin

Seems like the whole world is headed to hell in a fascist handbasket.

3

Soumik Mukherjee

@eternalfool please take a look at this counter example of your generalization chat.stackexchange.com/transcript/message/63431489#63431489

Alessandro Codenotti

17:54

What was the question?

PlaceReporter99

I think I discovered a new mathematical constant

It's the non-integer solution to $2x=x^x$

It would be hard to write the exact form so here is the Wolfram Alpha query for the formula.

anak

@PlaceReporter99 I don't think specifying a number is quite the same as discovering a new mathematical constant.

Cotton Headed Ninnymuggins

Let $d_i$ be the i'th digit of a natural number and $1\le i\le j$. Let a natural number be symmetric if for every $i$, we have $d_i=d_{j-i+1}$. For what $n\in \mathbb{N}$ is $11^n$ symmetrical? It seems $n=1,2,3,4$ work, how might you show there's no more?

PlaceReporter99

@anak ?

Cotton Headed Ninnymuggins

@PlaceReporter99 What's special about the number? Why not claim a new mathematical constant for $3x=x^x$?

PlaceReporter99

18:09

@CottonHeadedNinnymuggins Why don’t I create a sequence?

Cotton Headed Ninnymuggins

What kind of sequence?

Miss Mae

@anak the only economical thing I think most instructors should think about more is costs of books, and if there are books that are so advantageous that need is high for the class regardless of cost, the instructor should offer legal resources to assist students in finding alternative ways to get access to the book. ie. library loans, e-book discounts, MAA waivers, extended financial aid, etc. Math needs more free, open-access materials tbh

anak

@MissMae Yes, this is a good point. Being mindful of socio-economic status is always a good thing.

Miss Mae

18:26

The only reason that economic point stands out the most to me is that for a lot of low-income students in the US, their financial aid/scholarships start and stop with classes and sometimes rent, and almost always never include book costs. Had a student in one of my classes talk about how they had to sell a lot of their belongings for a book in their Engineering class, made my heart sink into the floor

Xander Henderson

@MissMae I have more instructor copies than I need, strictly speaking, and might have a habit of loaning them out to students.

Miss Mae

didn't hear if the book was actually used in the class or not, as some professors stress that a books is needed and then it's actually not used in the course, so I would like to think for the least it was hopefully used

Xander Henderson

@MissMae I use books for their exercises. I am close to having enough exercises of my own (with solutions!) for a precalculus class. Once I get all of the problem sets written, I will stop requiring a text for that class. I am optimistic that I'll be ready to go in the fall.

Though I've had so few f***s to give this semester, and have made little progress. :/

anak

@XanderHenderson when collecting and distributing problems (especially for something more basic like precalculus), do you find it necessary to keep track of where the problems are from and citing them? Or do you take advantage of the fact that it's fair use for educational purposes usually?

Xander Henderson

@anak I am not taking problems from other sources. I write my own.

Miss Mae

18:32

What one of my instructors has done is just copy the exercises from books and gives a bibliography at the end of each homework so she doesn't have to make the mook required for the class, but the whole class is her notes, so I feel like that's a good compromise

Xander Henderson

Not that there is anything particularly deep to write exercises about---I would guess that about a third of my problems are the same as those found in any text, modulo the specific numbers I use.

PlaceReporter99

What’s the degree of the polynomial $x^x$?

anak

It's not a polynomial.

PlaceReporter99

@anak is it a ‘hyper polynomial’ then?

I made that phrase up

anak

What is a hyper polynomial?

PlaceReporter99

18:43

Idk

just came from geometric series -> hypergeometric series

Cotton Headed Ninnymuggins

@MissMae Literally TONS of free textbooks here: libgen.is

Or try Googling "[textbook name, author] filetype:pdf"

Probably one of the most useful websites ever, I have saved a decent amount of $$$. Also, libgen doesn't have just textbooks either, but also free books in general and I have never not been able to find what I'm looking for

Xander Henderson

19:04

@PlaceReporter99 That function, to the best of my knowledge, does not have a standard name. It is neither a polynomial, nor an exponential, function.

But it is more like an exponential function than a polynomial function.

Related: en.wikipedia.org/wiki/Tetration

anak

@CottonHeadedNinnymuggins piracy isn't really something you can obligate your students to do, since that's technically breaking the law.

Soumik Mukherjee

chat.stackexchange.com/transcript/message/63428996#63428996 @AlessandroCodenotti this was the initial question and chat.stackexchange.com/transcript/message/63430268#63430268 was the generalization the user was asking about

Obliv

How does one convert $\int_0^{\sqrt{5}}\int_0^{\sqrt{5-x^2}}\sqrt{x^2+y^2}dydx$ into polar coordinates and solve?

PlaceReporter99

@CottonHeadedNinnymuggins Not just a sequence, but a function!: desmos.com/calculator/iilgl01ifp

Obliv

I set $r = \sqrt{x^2 + y^2}$ and the bounds describe a half circle I did $\int_0^{\pi}\int_0^{\sqrt{5}}rdrd\theta$ but got it wrong

Xander Henderson

19:15

@Obliv You seem to have forgotten the Jacobian.

Obliv

This section doesn't involve that concept yet

I'm pretty sure I have to use $y = r\sin \theta$ and $x = r \cos \theta$ but I don't get how

Xander Henderson

@Obliv The book may not call it that, but if you are changing coordinates, you are going to pick up an extra factor related to the Jacobian.

Semiclassical

$dxdy=rdrd\theta$ and all that jazz

Xander Henderson

$$\iint f(x,y) \,\mathrm{d}x\,\mathrm{d}y = \iint \hat{f}(r,\theta) \color{red}{r}\,\mathrm{d}r\,\mathrm{d}\theta,$$ no?

Obliv

yes but how do the bounds change?

Xander Henderson

19:18

(where $\hat{f}$ is just me trying to indicate that it is the same function as $f$, but written in polar coordinates)

@Obliv Your problem is not with the bounds of integration.

Obliv

From $0 \leq y \leq \sqrt{5-x^2} \to ?$

Xander Henderson

You left out the Jacobian.

You lost a factor of $r$ in your change of variables.

Obliv

ohhh

Semiclassical

It’s better to view this as a double integral rather than an iterated integral, ie, not worrying about the bounds on individual variables but on the integration region

(Tho that is indeed not the main point)

Miss Mae

@CottonHeadedNinnymuggins Thing is, while that is great and all, i’m betting that some of the content that is posted there wasn’t done with the authors or publisher’s consent, and the risk of a student getting caught by their university for accessing such resources may be minimal, if they were to get caught the punishment may be astronomical and may ruin their chances at being part of their program any longer

Obliv

19:21

Also it was a quarter circle somehow

I am missing a factor of 1/2 so I'm guessing it was supposed to be $\pi/2$

Miss Mae

it’s a risk vs reward system, and while a majority don’t get caught (or think they haven’t been caught yet) it can be dangerous for those who have a lot to lose (academic enrollment, housing, repayments if the publisher goes after you if they knew, etc)

Obliv

ah yea it's $\int_0^{\sqrt{5}}dx$ makes sense

volume of a solid bound between $z = xy^2, x^2 + y^2 = 9$ first octant. What even is $z = xy^2$ the graph of?

I put it into wolfram and it looks like a weird bendy sheet

If I wanted to find this volume I guess I don't have to worry about what's on top or bottom or whatever

oh wait yeah $z=xy^2$ gives the $f(x,y)$ and that's constrained above the circle of radius 3 in the first octant

Obliv

19:43

If I'm given $Q$ given by $x + y + z = 10, x=0,y=0,z=0$ and I'm asked to find the mass with $\rho(x,y,z) = k$ , how would I set up the integral?

$\int \int \int_0^{10-x-y} k dz $ I think i got the innermost integral ?

so i get $\int \int k(10-x-y)$

nvm I got it

Alessandro Codenotti

20:20

@SoumikMukherjee a more interesting question is whether $[0,1]^2$ can be written as $X\times Y$ with $X,Y$ not homeomorphic to either a point, $[0,1]$ or $[0,1]^2$ rather than just asking for them not to be literally a straight line

Soumik Mukherjee

@AlessandroCodenotti yes

D.C. the III

22:19

Is your reasoning for putting in the question $\int_{\mathbb{R}^3} e^{-(x^2+2y^2+3z^2)}dV$ to remind us to not jump right to polar/spherical coordinates without thinking @TedShifrin ?

Ted Shifrin

Not particularly. Just a way to apply the results on the integral of the Gaussian.

D.C. the III

fair enough. That's what I did....well actually it is the only way I know of doing it....

Transcript for

$Mathematics$ Mathematics