Mathematics

6:02 PM

Hmm. Let me phrase is another way. If a condition is true for a set $A$, it is true for all subsets of $A$. It has something to do with the structure of the set $A$. For example, if a set $A$ is a group, then not all subsets of $A$ are groups. Here $f$ would be a function which checks if the argument is a group or not.

But now, suppose there is some property of a set $X$ determined by its structure and the situation is if a set $A$ satisfies that property, then so do all subsets of $A$ satisfy that property, is there a name for such thing?

Jonas Teuwen

@MarianoSuárez-Alvarez No.

Ilya

@OrangeHarvester so, you mean $f:2^\Omega\to \{0,1\}$ where $\Omega$ is some universal space. Suppose, there is $A\in 2^\Omega$ such that $f(A) = 1$ implies $f(X) = 1$ for all $X\subseteq A$, right?

Jonas Teuwen

Do you need tensors, tensors for your products Ilya?

My advisor loves tensors. We tried to outclass each other in loving tensors.

Mariano Suárez-Alvarez

@JonasTeuwen :)

Jonas Teuwen

In terms of number of pages he won... but...

Orange Harvester

6:07 PM

@Ilya Hmm. Kind of. I just realized then, it would have to be true for every singleton set then. So, what you wrote before was correct. But my actual question was different. Let me rephrase that again, and see if I can do that. :-)

I will take my time this time.

Jonas Teuwen

It is only not so good to be attracted to me as I barely can stand myself! If I would ever commit suicide and write a note, it would be "life is too long to spend with assholes".

Mariano Suárez-Alvarez

well, use that as a conversation starter and he'll probably stop :P

Jonas Teuwen

:P.

That is a 9.2 on the scale of rhetorics.

Mariano Suárez-Alvarez

who punctuates a smiley?! :D

Jonas Teuwen

I got a 9.95 a couple of weeks ago when a student mailed me and asked how you decide which method of integration has to be used for a given problem.

So I replied in a formal way and stated: 'Such a trick indeed exists. It is called: thinking. It also works in many other occasions. Perhaps you should give it a shot!'

@MarianoSuárez-Alvarez I always do.

Mariano Suárez-Alvarez

6:15 PM

integration is had on students because there are no rules

(at least, they are never taught any)

Jonas Teuwen

There is a rule, it is called practice!

Mariano Suárez-Alvarez

usually abstract linear algebra has the same effect, as it is the first abstract thng the learn and proving things about that is sort of free-form

yeah

Jonas Teuwen

The same holds for differentiation: you need to spot the pattern.

Mariano Suárez-Alvarez

while it is obvious for you, it is not for many

Jonas Teuwen

And the rest is a mechanical trick, just as with integration but perhaps a bit harder, but the exercise you get...

Yes, that he asks such a question is 1) He did not listen to me saying it every class 2) No practice.

Mariano Suárez-Alvarez

6:17 PM

in any case, telling people to think has the same effect as telling them «not to worry»

that is, none :)

Jonas Teuwen

If the question would be more specific in 'how to do <...>'.

Mariano Suárez-Alvarez

but asking specific, precise questions is also an art

Jonas Teuwen

Yes. But I take offense in him not listening to me while I told him personally two times before.

Mariano Suárez-Alvarez

you have to teach them to do it

Jonas Teuwen

Additionally, there are ~100 students and I am able to remember what they asked me, why they not what I told them personally.

Right, but they are not mathematics students and my task is to teach them calculus, not to be scientists. Other people are more qualified for that.

Mariano Suárez-Alvarez

6:19 PM

asking correct questions is part of calculus

Jonas Teuwen

Mm, not here (for engineers). Here is this integral. 'Solve' it.

Mariano Suárez-Alvarez

i am of the opinion, in fact, that teaching calculus is only useful to have some excuse to teach people how how think

well, if you teach them that way, you get what you got

Jonas Teuwen

How can you do that with so many?

I do have two BSc and one MSc student, that is much cooler.

In a one-on-one discussion you can do that.

Mariano Suárez-Alvarez

it is much easier to teach people who are interested and motivated and know stuff

restricting one's effort to them is cheating, in a way

Jonas Teuwen

Yes, and I do not feel like it is my task to motivate them to study for the thing they like to do. I give interesting examples and different explanations.

The effort is lost in thin air, I prefer to spend that on people that actually do care! Like those two (not the third).

Mariano Suárez-Alvarez

6:21 PM

most people with the interest and motivation in fact could do without us

it is the others that need the help

Jonas Teuwen

Mmm, they can do without, but they can make much quicker progress with help.

In any case, independent of the lecturer more than 60% fail for the exam the first time.

Mariano Suárez-Alvarez

sure

but passing the exam is only part of it

Jonas Teuwen

That is all the care about.

Mariano Suárez-Alvarez

lots of people pass examsn and do no tunderstad anything

Jonas Teuwen

'Is this on the exam' when you explain a cooler example.

With the answer 'no', most drop the pen.

Yes, as they do not care.

Mariano Suárez-Alvarez

6:23 PM

cool examples are mostly a mastubatory activity on the part of the teacher

Jonas Teuwen

And I do not think it is my job to make them care.

Perhaps your cool ones are.

In this particular case it was giving some intuitive reasons why infinite sums of positive things can still be finite (by filling up a circle or so).

Mariano Suárez-Alvarez

if you give an example and it is lost on 76% of the class, and you know this, then the example was more or less pointless

Jonas Teuwen

With 'cool' I mean 'not in the book'.

Mariano Suárez-Alvarez

if they are going to be evaluated by what is in the book, and they know this, it is understandable that they do not care

Jonas Teuwen

I have no intrinsic reason to want to look or sound smart.

Yes, but they don't understand that either - no matter what you do.

Mariano Suárez-Alvarez

6:25 PM

trust me, it does matter what you do

Jonas Teuwen

Okay - well, there are about 30 lecturers and all have about the same pass rate...

Mariano Suárez-Alvarez

if there is one thing that has given me hope in humankind is seeing what students do

Jonas Teuwen

(same course across faculties)

Do shit? - Not make war.

Mariano Suárez-Alvarez

if you really think there is nothing useful you can do, you might just as well do something else

teaching without faith is one of the worse activities there are

Jonas Teuwen

Like you are at the same party where most of the class is and the next morning in the lecture there is... one.

Indeed, so I do.

But I do not have the complete choice in that.

The 1-1 and research with the students is more fun.

Orange Harvester

6:27 PM

@JonasTeuwen What do engineering undergraduates undergo in math at TU delft? Proper analysis and linear algebra courses or a complete medley compressed into "Engineering Mathematics" on the line of Kreyszig?

Jonas Teuwen

@OrangeHarvester The latter :S.

Orange Harvester

Well, then I feel that is a part of the problem. (Having undergone the kreyszig thing myself.)

Jonas Teuwen

Depends - mathematics engineering go do some Springer GTM in the undergrad.

Yes, my advisor too, he even said it in his inaugural lecture 8-).

But one cannot chose the book. It is how it is.

Here is the schedule, do that.

Orange Harvester

Same at my uni it was.

Jonas Teuwen

And then 'don't bother too much, they will not listen anyway'.

Complex analysis for mathematics students was much better.

They actually ask a question which you can't read directly from the book 8-).

Orange Harvester

6:31 PM

That is cool.

Jonas Teuwen

And I do not know how I should 'motivate' people which do not want to be motivated.

Mariano Suárez-Alvarez

Well, I don't

Jonas Teuwen

I do not feel that is my task. They come there to learn something, then I will help them with it, but if they come there to just sit through the lecture and play games or whatever...

Mariano Suárez-Alvarez

I just treat them all like they are motivated

Jonas Teuwen

Even the ones that immediately open laptops?!

Mariano Suárez-Alvarez

6:32 PM

I'd ask them to leave

Jonas Teuwen

Yep, then next time the class is empty.

Mariano Suárez-Alvarez

well, so be it

explain to them what you expect from them

Jonas Teuwen

It is different with the physics students or aerospace engineering.

Mariano Suárez-Alvarez

they'll respect you for that

I expect attention

all my students know it

Jonas Teuwen

Yes, that does not work with these.

Mariano Suárez-Alvarez

6:34 PM

they are free to come or miss my classes

Jonas Teuwen

With the physics students it does.

Mariano Suárez-Alvarez

and i have explained many times that I simply do not care if they do not come

Jonas Teuwen

The ones I talk about are from @Ilya his faculty.

Orange Harvester

@MarianoSuárez-Alvarez Well, here we have "compulsory attendance" :P

Jonas Teuwen

It's like the girl scouts.

Mariano Suárez-Alvarez

6:34 PM

If I had compulsory attendance, I'd make them as present and tell them they can leave

Jonas Teuwen

We once had a very old professor. Very sour face.

Orange Harvester

Yeah, some profs do that.

Jonas Teuwen

And then some students talked to each other and laughed. He said: 'What is so funny? I like to laugh too :|'

'Knock know' Who is there? 'There is the door.'

I still prefer the 1-1.

Mariano Suárez-Alvarez

it s a different game

Jonas Teuwen

As it really helps, not many bachelor students manage to get up to locally convex spaces and quantum fields.

(And write a paper about it too)

Alright, I go to a party. Tensor or categories, which book to take.

Orange Harvester

6:39 PM

Tensor.

My idea is to restructure the course. We are taught about beta functions and we do not get to use or even see them until we are well into masters program. And by that time, the analysis background is not good enough that the special functions can be learnt on their own. I would rather say that teach them some more basic hard core techniques in analysis and then trust the people to learn the special functions themselves when they get into masters course. Similarly for linear algebra.

But of course you said that is not possible, which is a shame, but if it helps, you might now understand their perspective.

Jonas Teuwen

Special functions are so fun.

Tensor is a bit tough in the evening, I'll take the categories.

Orange Harvester

They are fun only if you know how to navigate around them.

Jonas Teuwen

I used an ${}_1\!F_1$ to improve a doubling estimate in harmonic analysis :P.

Orange Harvester

Cool. Without the navigation skills, they are bunch of instructions, and if you get on wrong, you are lost.

Jonas Teuwen

Try harder then.

I leave, so see you later! Enjoy your day/morning/evening/night.

Orange Harvester

6:43 PM

Later!

Nimza

7:24 PM

Hello! What does mean operation "#" between topological spaces?

anon

knot sum?

Novice

Why did the troll remove that $2$...

Another upvote. Why God, why

Somebody is downvoting and upvoting

And now that chat message doesn't make sense at all.

Nimza

@anon connected sum :)

Ilya

7:47 PM

@Jonas: what. You talk about 3mE students and mentioned my name?

Ethan

7:57 PM

How can I prove that$$\sum_{k=1}^nx^{\gcd(k,n)}=\sum_{d\mid n}\phi(\frac{n}{d})x^d$$

anon

gcd(k,n) is always a divisor of n, and for any divisor d|n the number of k such that gcd(k,n)=d is equal to the number of generators of the unique cyclic subgroup of order n/d in a cyclic group of order n (since the order of k in Z/nZ is n/gcd(n,k)), which is equal to phi(n/d)

Ethan

nvm i see

Ok I understand it all, except why is the number of $1\leq k\leq n$ such that $gcd(k,n)=d$ equal to $\phi(\frac{n}{d})$

I know the special case d=1 is true

because thats how I define the phi function

nvm I just proved that, thanks for the help anon

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$Mathematics$ Mathematics