Mathematics

SteamyRoot

8:00 PM

Oh, wait, maybe I misinterpreted and you wanted $2p(x)$. Hrmf.

Typhon

@SteamyRoot what are you trying to tell me? A user sent me a random post and I replied to it...

i dont want anything

i was told to answer it

SteamyRoot

I know. And I'm saying your solution looks wrong.

Typhon

@SteamyRoot what I'm saying is that I really don't care. I'm honestly confused as to why I was even sent the problem to begin with. It seems trivial.

SteamyRoot

Fair enough.

Typhon

@TedShifrin hello

Ted Shifrin

8:07 PM

howdy

Typhon

@SteamyRoot would you say this is a duplicate post? Seems a bit of a stretch to me

5

Q: Are all solutions to an ordinary differential equation continuous solutions to the corresponding implied differential equation and vice versa?

Now I have to heavily emphasize the fact that I have never studied differential algebra or the concept of other types of differentiation (which is what I believe is the concept behind a differential algebra). So, if I am abusing the terminology a little bit, please forgive me. Let us define a di...

hi chat

heya ERic

Hi Ted

i must be missing something here?

they're two different conjectures...?

Ted Shifrin

8:09 PM

Hi @Astyx ... done with more exams?

Astyx

4 days to go

(and a half on the 18th)

Eric Silva

how long do your exams last

Astyx

Too long

I've had 2 weeks already

Eric Silva

oh my god

Astyx

And I'm supposed to take two more weeks

Eric Silva

8:10 PM

so a marathon as opposed to a sprint like it is here

Astyx

But I think I'll skip the last

Rather a series of 4 sprints over 3 miles

Eric Silva

oh god sounds awful

Astyx

It is

Luckily I have my morning tomorrow

I'll be able to catch up all the sleep I'm missing

Eric Silva

im historically a good tester but honestly i hate exams

Ted Shifrin

I used to like 'em

Grading exams and listening to panic attacks for the last 40 years was way worse than my taking them.

Eric Silva

8:12 PM

i reeeaaally like take home exams though

Ted Shifrin

Any take-home exams I wrote were way harder than any in-class exam.

Eric Silva

yeah they gotta be

like i would like it if exams were like really difficult psets

Neves made his final a take home and put really hard problems on it

but i guess the drawback is that it's probably way harder to grade my 15 page take home final than it was to grade a bunch of 4 page exams

Astyx

Exams seemed alright until now

Ted Shifrin

indeed

Eric Silva

I'm very proud of how well i did on that final

i got a 98 and the average was in the 60s

Astyx

8:16 PM

I made my decision about X/ENS btw.

Ted Shifrin

plus, except for a few advanced courses, I wanted a final exam to check that students knew the definitions and the basics, not super-tricky stuff like on problem sets.

that's pretty good, Eric ...

Eric Silva

that's a super fair point @Ted

ive never done as well in any class as i did in Neves Riemannian geo

Ted Shifrin

despite my reputation, I tried to be demanding but fair

Eric Silva

@Astyx what did you decide?

Ted Shifrin

you were more into his class than probably most others

Eric Silva

8:17 PM

that's def true, I was suuuuper into it

i spent lots of my free time thinking about the course material

Astyx

To pursue my maths interest and not care about other people/money

Thus the ENS

SteamyRoot

:D

Astyx

(that's if I get the opportunity obviously)

Typhon

lol

Ted Shifrin

well, ok, at least you done did made a decision

Eric Silva

8:18 PM

cool

Typhon

i just learned why you don't reuse a paragraph at the intro of two questions

because then lazy people will think they are duplicates

Eric Silva

what's the curriculum like at ENS

SteamyRoot

Well, frankly, if you have nearly identical question names and they start in a nearly identical way, it's kind of to be expected?

Eric Silva

i imagine it's really intense

Typhon

no

heck no

the paragraph that is the same is the definition of an operator

everything else is totally different

Astyx

8:20 PM

Make sure that's apparent in the title and you should be fine @Typhon

@EricSilva You have a choice between multiple courses in a broad spectrum of subjects

SteamyRoot

Or write at the top of your question what the difference is between your previous question and this one

And why this merits to be its own question and not an edit of the former question.

Typhon

dude

the question that was closed

is the older one

Astyx

(maths, physics, litterature, economics, philosophy etc)

Typhon

@SteamyRoot that is always a horrible thing to do

you shouldn't have to justify a question

or prove it is different

SteamyRoot

Well, the moderation backlog is also quite the horrible thing.

Typhon

8:22 PM

@SteamyRoot it's not moderation

it's user's closing posts

Eric Silva

@Astyx i meant more along the lines of: What's the standard stuff all the math students have to do

Typhon

and the user that initiated it hates my guts anyways

chances are they already voted to delete like normal

eye roll

Astyx

@EricSilva That's the beauty of it : you don't have to do anything :p

(unless I'm mistaken)

Eric Silva

really?

Astyx

I think I could only take litterature courses even though I never got good grades in French in my life and that I come from the scientific door into the ENS

I could also do Design

SteamyRoot

8:24 PM

It doesn't have to be a proof or anything. A short justification "this question differs from question blah blah in that here we limit ourselves blah blah" whatever.

Eric Silva

at my institution all the math students have to take a year of algebra + a year of analysis + 2 upper division math electives (topology, algebraic topology, PDE, functional analysis, complex analysis) and so on

Typhon

@SteamyRoot exactly

those edits only clog up question

in fact, whenever I see those things I remove them

SteamyRoot

Sigh. Nevermind.

Typhon

also

the newer question does have such a statement

Astyx

@EricSilva That's probably what I'm going to do, but that's only because I want to

Eric Silva

8:25 PM

oh they have to take a linear algebra class too now i guess, I skipped that

Typhon

and yet the older one was closed

oh and here's something interesting for ya

when it was closed

that statement was edited out by the user that closed the post

Eric Silva

@Astyx cool

Typhon

in other words, they removed it so it would get closed

SteamyRoot

If you think that's unfair, contact a moderator.

Typhon

i did

Eric Silva

8:26 PM

idt I have a good sense of what all math students who want to try to pursue academic things should know

Typhon

mods dont do shit

Sir Cumference

My sister is having an existential crisis about math and won't talk to me

Someone please answer her question, I'm letting her talk

Astyx

@Eric "idt" ?

Eric Silva

i don't think

Astyx

Oh right, that completely changes the meaning :p

Typhon

8:27 PM

@SteamyRoot they were asked a month apart.

Astyx

Anyway, high hopes

Sir Cumference

Hi, quick question. I'm in calculus and when dealing with limits, we often have to simplify or rewrite functions to solve them

Astyx

I probably wont be accepted in the school anyway :p

Eric Silva

lol @Astyx im only a rising third year undergrad, im still a neophyte who has a lot to learn

i wish you luck on your admissions though

Astyx

I think I'll always be a neophyte who has a lot to learn

Thanks !

SteamyRoot

8:29 PM

@Astyx Oi, don't be so negative! :P

Sir Cumference

But how can a function give me indeterminate form when written one way, but give me a proper limit when written another way?

Tobias Kildetoft

@Typhon Which question is this? I could not find which one you are referring to on your list of questions

Sir Cumference

Shouldn't both forms be identical?

Astyx

Truth is, I have no idea wether I'm among the best that are taking the oral exams.

Typhon

5

Q: Are all solutions to an ordinary differential equation continuous solutions to the corresponding implied differential equation and vice versa?

Regarding the duplicate. Yes, I know the other one has a lot of shared text, but those were just definitions/setup and I was being lazy. The core questions are still different unless you believe derivatives are weak derivatives in which case you might need to read up on them. I don't know the exa...

differential-equations limits derivatives differential-algebra

3

Q: Are all weak solutions to an ordinary differential equation continuous solutions to the corresponding implied differential equation and vice versa?

Yes,this is very similar to a previous question I asked. That was about normal solutions and not weak solutions. We define the operator known as the implied derivative denoted as $I(f)(x)(g)$ to be: $$I(f)(x)(g) := g(x) \left(\lim_{h\to 0^+} \frac{f(x+h)-f(x)}{h} \right) + (1-g(x)) \left(\lim_{...

calculus differential-equations floor-function weak-derivatives piecewise-continuity

Astyx

8:30 PM

For polytechnique I have some idea, for the ENS I have absolutely no clue

Eric Silva

how many people are vying for admission?

Astyx

147

GFauxPas

@sir what is a "proper limit"

Astyx

They only take 40

SteamyRoot

@SirCumference I'm guessing your problem is about, like, why $\lim_{x \to 0} \frac{x}{x} = 1$ by cancelling out $x$, even though pluggin in $x = 0$ gives $0/0$ ?

Sir Cumference

8:32 PM

Sorry, I mean to actually get the limit and avoid indeterminate form

Typhon

@TobiasKildetoft i posted them. Definitely in the same field, but not the same conjectures.

one is false

Sir Cumference

Yeah, steamy

Typhon

one is questionably true

GFauxPas

I wrote a page on this, one sec

Sir Cumference

Aren't the two mathematically identical?

Astyx

8:32 PM

However since some chose polytechnique over the ENS, the last called is among the 90 first

SteamyRoot

Technically, they aren't. $x/x$ is undefined in $x = 0$

GFauxPas

proofwiki.org/wiki/Limit_of_Functions_that_Agree Sir this is the formal reasoning why, but i dont think it gives you intuition

Eric Silva

@Astyx only 40? how big are these schools

Astyx

87 to be precise

SteamyRoot

But on every other $x \in \mathbb{R}$, they are identical.

Typhon

8:33 PM

nvmd

Astyx

@EricSilva They are very selective (note that I'm only talking about the ENS Ulm, there are 3 others) which partially explains their internationnal success

Typhon

@SteamyRoot are you real good with math and stuff?

i need help writing out better logic

SteamyRoot

The intuitive idea is pretty much that a limit of a function in a point isn't (just) determined by that point itself, but largely by the surrounding points.

Sir Cumference

@SteamyRoot but for example, you sometimes need to rewrite a function into something equivalent, before you can solve it

Astyx

So not very big

SteamyRoot

8:36 PM

@Typhon Dunno. Depends on what area of math.

Eric Silva

my school has like 5000 people in the undergrad @Astyx, but we accept something like 7% of people

Sir Cumference

I think the proof for either the product or quotient derivative rules requires you to add a term to the numerator, which evaluates to zero

Eric Silva

so 30000 people usually apply in recent years but like 2000 something get in

Typhon

@SteamyRoot sets/integrals

Sir Cumference

But adding it allows you to cancel things out and find the limit

Typhon

8:37 PM

0

Q: For all ordinary differential equations, does there exist a corresponding integral equation?

My second conjecture here does have some logic issues. The problem is that I am not sure how to express the idea of looking at integral equations under equivalency classes based on the solution sets being equal. Please see the comments of the current answer. Such logic is beyond my set theory abi...

integration differential-equations elementary-set-theory conjectures

Eric Silva

and then there's attrition

so not everybody comes

Typhon

im trying to use set theory to convey the idea that out of all sets corresponding to integral equation solution sets, there is only one that is a superset of the solution to a differential equation while having the smallest set magnitude.

and I know that has to have at least one loophole. XD

but if someone could please help rewrite the logic so that works correctly and makes sense, please edit my post

SteamyRoot

@SirCumference That might be the "$\lim f(x) + \lim g(x) = \lim f(x)+g(x)$ in disguise, then?

Astyx

There were 1600 persons taking the written exams last year, they only kept 10% for the oral exams, and only 25% of those actually got in

Which explains my stress :p

Eric Silva

wow

it's very different

Sir Cumference

8:40 PM

Wait, it was the product rule

Eric Silva

we have no exams but we submit college applications and they get reviewed by like teams of people holistically and honestly it seems like it's mostly just luck if you've got the stats to get in

Sir Cumference

At some point, you add f(x+h)g(x) -f(x+h)g(x), if you are taking the limit as h goes to 0

Eric Silva

my school is one of the most selective ones in the states but honestly it seems like admissions is like a black box that you dont really undesrtand unless youve seen directly how it works

Astyx

Any admission strategy relies on luck at some point

Eric Silva

sure

Semiclassical

8:46 PM

hi chat

Astyx

hi Semi

Semiclassical

Any good math today?

Typhon

not really

just weird close votes

Astyx

If $f : \Bbb R^2\to \Bbb R^2$ is $1$-lipschitz for the eculidean norm, prove ${1\over n}f^{\circ n}(x)$ converges to a limit that does not depend on $x$

Typhon

@Semiclassical you could probably help me out

0

Q: For all ordinary differential equations, does there exist a corresponding integral equation?

My second conjecture here does have some logic issues. The problem is that I am not sure how to express the idea of looking at integral equations under equivalency classes based on the solution sets being equal. Please see the comments of the current answer. Such logic is beyond my set theory abi...

integration differential-equations elementary-set-theory conjectures

not sure how to fix the troublesome logic

Astyx

8:53 PM

Bye chat