The h Bar

0ßelö7

2:31 AM

@dmckee why is fortran so punishing

Abcd

2:49 AM

@Blue 80%. Will take time to understand the 20% part

Alfred Centauri

3:08 AM

@heather, physics.stackexchange.com/questions/359323/…

dmckee

@0ßelö7 Depends on the fortran you're learning I guess, but basically because it has a legacy that stretches back to before people knew what made a language comfortable to use and expressive.

It has too many ways to do some things and not enough to do others, plus it's bondage and discipline in all the wrong places.

0ßelö7

@dmckee what is with this ridiculous rule that you can't declare variables after you execute a command

I had to make a subroutine to declare an array

it's awful

Abcd

Is there any difference if I write $\Delta U = \Delta Q + \Delta W$ instead of $dU = dQ +dW$? My chemistry teacher said that both are correct ways but still I am uncertain.

Semiclassical

First is right, second isn't

$Q$ isn't a state function. So $\Delta Q$ depends on the path you take.

0ßelö7

@Semiclassical Only took me 3 hours to get fortran to spit out fibonacci numbers

Alfred Centauri

3:21 AM

@0ßelö7 please submit your question on punch cards

2

Semiclassical

:0

Abcd

@Semiclassical So?

0ßelö7

to be fair about 1.5 of that was because I never actually read in a parameter :)

if I were using Matlab it would have told me that!!

Semiclassical

If you write it as $dQ$, you might think you can write $\int_{t_1}^{t_2}\frac{dQ}{dt}\,dt=Q(t_2)-Q(t_1)$.

Abcd

@Semiclassical So which is more apt $\Delta Q $ or $dQ$?

Semiclassical

3:25 AM

For a better discussion, see here: chemistry.stackexchange.com/questions/22171/…

Neither. I'd do $\Delta U=Q+W$.

$U$ is a state function, so $\Delta U$ is meaningful.

Huh, \text{đ}:$\text{đ}$ isn't something I've seen before.

Abcd

@Semiclassical Two of my freaking chemistry textbooks wrote $\Delta Q$ and $\Delta W$

@Semiclassical U can use partial differential I guess

It was given in a good physics book.

$ dU = \delta Q + \delta W$

Semiclassical

I'm more okay with that one.

Abcd

What's the difference between $\Delta$ and $d$?

Semiclassical

Differential versus difference.

Abcd

Both mean change...d means infinitesimally small change..

Semiclassical

3:28 AM

Right.

Abcd

@Semiclassical Why not d with the U here?

Semiclassical

Just pulled out my old chemistry textbook, and it gives the first law of thermo as $\Delta E=q+w$

because it's $Q,W$ for a finite change, not an infinitesimal change. So there's an initial energy $E$ and a final energy $E+\Delta E$.

0ßelö7

lol who keeps a chemistry book?

Semiclassical

I'm not good at getting rid of books.

0ßelö7

@Semiclassical I've got all of my physics books, but I don't think I've ever owned a chemistry book...

Abcd

3:31 AM

@Semiclassical Then why does the physics textbook use $dU$?

Semiclassical

i had to take gen-chem for my undergrad physics degree IRC

0ßelö7

AP tests!

Abcd

and chemistry textbook uses $\Delta U$

0ßelö7

@Semiclassical So we decided that the $\sqrt{z^2-c^2}$ should be interpreted as $\sqrt{z-c}\sqrt{z+c}$. When I take the derivative, should I do the single one or the double one?

Semiclassical

well, was the physics version $dU=\delta Q+\delta W$?

Abcd

3:33 AM

@Semiclassical yes

Semiclassical

then that's intended as a infinitesimally small change vs. chemistry doing a small but finite change.

Note, though, that the version that leads to in a physics textbook is this one:

$dU=T dS-pdV$.

Abcd

ok

Semiclassical

And $S,V$ are state variables, so using differentials here is fine.

test: $\dbar$

aw

0ßelö7

@Semiclassical yeah I need to put a bar on $d$ like $\hbar$

Semiclassical

$đ$

i stole that from the answer i linked, but it's not that great.

0ßelö7

3:42 AM

in harmonic analysis it's often convenient to take the measure to be $(2\pi)^{-n/2}d\mathscr L^n(x)$

and that's like an hbar normalization

so dbar

Semiclassical

nice

0ßelö7

@Semiclassical that way there's no stupid 2pis in Fourier transforms

Semiclassical

and then a gaussian distribution is really just the gaussian, hah

(as in, gaussian * dbar)

0ßelö7

@Semiclassical is this unicode?

Semiclassical

no clue. I just right-clicked what they'd used.

@0ßelö7 eh, this works though it's a bit involved: tex.stackexchange.com/questions/203508/…

0ßelö7

3:48 AM

$\newcommand{\dbar}{d\hspace*{-0.08em}\bar{}\hspace*{0.1em}}$

$\dbar$

doesn't work in chat

Semiclassical

nope

test: $\mathchar '26 \mkern-11mu d$

nooope

0ßelö7

works fine in latex tho

Semiclassical

test: $d\hspace*{-0.08em}\bar{}\hspace*{0.1em}$

this is one of those mathjax vs. latex issues, I guess.

0ßelö7

Semiclassical

nice.

0ßelö7

3:50 AM

I need to smuggle this into my fluids homework somehow

Semiclassical

just randomly replace regular d with unicode dbar for fun

Alfred Centauri

4:02 AM

@0ßelö7 Who doesn't? i.stack.imgur.com/r3pax.jpg

0ßelö7

@AlfredCentauri I used the 6th edition of that book

@Semiclassical Soooo...I have concluded that the coordinate transformation has no effect in the end. The far-stream is still $U$ and the circulation is still $\Gamma$.

So the disk flow has the same lift as the elliptic flow.

Semiclassical

hmm

that seems a bit odd.

0ßelö7

@Semiclassical If I write up the details will you read it?

Semiclassical

though, do you mean: that particular transformation has no effect, or conformal transformations in general have no effect?

0ßelö7

This particular one, I think.

Semiclassical

4:10 AM

hmm

I don't have a clear intuition for this, so shrug

0ßelö7

It makes sense because in the limit $|z|\to\infty$ one expects the flow to behave as a disk flow with radius $(a+b)/2$

Semiclassical

is it obvious it should be $(a+b)/2$?

0ßelö7

"far away" the ellipse looks like a disk

@Semiclassical maybe not

Semiclassical

Yeah. I think there's a way to make it more obvious, but in terms of units and symmetry it seems sensible.

I had initially expected $\sqrt{ab}$, since a circle of that radius has the same area as an ellipse with $a,b$ as semi-major/minor axes. But I think I convinced myself why that's too naive.

0ßelö7

@Semiclassical uh, how does one typeset the j unit vector

Semiclassical

4:16 AM

\hat{j}

dmckee

@0ßelö7 Well, this is another legacy thing. The original version of FORTRAN were written with simple model of compilation in mind: if you force declarations to the beginning compilation is easier and—crucially—can be made to take less memory.

The (lack of scale) of the main memory available to those machines has to be experienced to be disbelieved.

Thus @AlfredCentauri's comment about punch cards.

C had a variant of that 'feature', too, until the '99 standard.

0ßelö7

@Semiclassical seems wrong

shouldn't the right have something bold?

Semiclassical

$\hat{j}$

dmckee

@0ßelö7 Oohh ... I have a macro for that somewhere.

0ßelö7

is $\mathbf j$ ok?

Semiclassical

4:18 AM

oh, that typesetting

yeah, that's what I'd do

I kinda hate i,j,k as unit vectors now

$\hat{x},\hat{y},\hat{z}$ just seem so much easier

0ßelö7

@Semiclassical do you use $\mathbf e_k$?

Semiclassical

if I'm doing vector calc stuff, I tend to do $\hat{x}$ etc.

though i guess not if i'm using bold for vectors

0ßelö7

@Semiclassical i see

@Semiclassical I like bold for vectors in physics

Semiclassical

so do I, usually

0ßelö7

in fluid mechanics you can't get away with being sloppy because there's a difference between $\boldsymbol\omega$ and $\omega$, for instance

Semiclassical

4:22 AM

I do like being able to do $\vec{x}$ and $\hat{x}$

0ßelö7

@Semiclassical ok here's my final answer to the problem i.gyazo.com/585ff7678b9b754df02c00256e4e7be6.png

I don't know if I should take him up on his offer to turn it in late or just do it now

Semiclassical

Did you say he'd be doing most of that problem in class?

0ßelö7

Yeah, but, I have to do it anyway

and I have the proof on paper

Semiclassical

right

0ßelö7

his hint about the vorticity just being the jump over sheets on the Riemann surface was good

Semiclassical

4:24 AM

yeah, write it up. if he's going to present the details in class prior to you having to turn it in, then you can use that to check what you've got

Yeah, Log is merciful in that regard: If you evaluate $z$ on different branches, then the answers can only differ by an integer multiple of $2\pi i$.

0ßelö7

someone should do a flow with a lambert function :P

Semiclassical

you joke, but

you use $x\mapsto xe^x$ as a conformal map to get the electric field lines at the edge of a capacitor

0ßelö7

oh god

Semiclassical

see page 3 of this for instance: ir.lib.uwo.ca/cgi/…

0ßelö7

that's scary

Semiclassical

4:28 AM

yuuup

0ßelö7

for some reason no matter how much math we learn, special functions are still scary

Semiclassical

yeah.

actually, I know at least one property of the Lambert-W function which I don't know a good explanation for

Cows

@0ßelö7 sorry for the late reply. I am doing pretty well too these days .

Semiclassical

namely, this one:

5

Q: Smoothness of $\frac12[W_0(x)+W_{-1}(x)]$ for real $x<0$

The Lambert W-function, i.e. the multivalued inverse of $z=we^w$, has countably many complex-valued branches $W_k(z)$. The relations between the branches are a bit involved and are summarized here. We will consider the behavior of the $k=0,-1$ branches for $x<0$. Using Mathematica, we obtain the...

Cows

@vzn :D hehe

0ßelö7

4:30 AM

only 12 pages of scratch work for this homework

jeez

Semiclassical

on that note, one of my students sent an email to me and the prof saying that they thought the HW was still too long :)

0ßelö7

@Semiclassical blinks

I have to read that again lol

Semiclassical

lol

look at the pictures

that makes it more obvious

0ßelö7

ok, those plots are along the x-axis

@Semiclassical I am red-green color-blind. I see no green curve.

Semiclassical

yeah. hrm. that wasn't really clear, in retrospect

:(

lemme make a version of that with the green curve replaced by black

0ßelö7

4:35 AM

thx

@Semiclassical is it too long?

Semiclassical

I think it's not too long as much as too hard

0ßelö7

what class?

Semiclassical

the problems he put at the end have simple solutions, but they're not obvious

quantum mechanics

0ßelö7

simple solutions in QM = conceptual questions?

Semiclassical

One of the problems is when you take the harmonic oscillator potential and cut it in half (i.e. $V(x)=\infty$ for $x\leq 0$)

0ßelö7

4:37 AM

oh god, that question

Semiclassical

lol

0ßelö7

I get the feeling that every QM class has the same homework problems

Semiclassical

they really do.

in retrospect, I wish he'd posed it in a less 'harmonic oscillator' way

namely: "Suppose you have a symmetric confining potential $V(x)$ with bound states $\psi_n(x)$, $n\in \mathbb{N}$. If I cut $V(x)$ in half, what are the solutions?"

0ßelö7

@Semiclassical I hope to one day teach a functional analysis topics course on QM and put sneaky problems like that on the HW and watch the math students suffer :)

Semiclassical

the second problem was to solve the harmonic oscillator in the momentum representation

0ßelö7

4:40 AM

@Semiclassical I knew this a semester ago, what's the answer?

Semiclassical

well, all the states $\psi_n(x)$ satisfy the Schrodinger equation for $x\geq 0$. so the only question is one of boundary conditions

0ßelö7

is it all of the ones with $\psi(0)=0$?

Semiclassical

right.

and there's an obvious class of solutions which will do that; namely, the odd eigenfunctions

0ßelö7

yep

Semiclassical

moreover, an odd eigenfunction with $2n+1$ nodes for all $x$ will have only $n$ nodes for $x>0$.

0ßelö7

4:42 AM

@Semiclassical So in my elliptic PDE class the prof wants us to do presentations on "papers relating to the subject and they can be from your research"

Semiclassical

so you get a ground state with no nodes for x>0, a first excited state with one node, etc

so you're definitely not missing any eigenfunctions by doing this.

0ßelö7

@Semiclassical aha

the node theorem seems key there

Semiclassical

well, you can also do it by looking at the analytic solution of the harmonic oscillator

0ßelö7

@Semiclassical so I think that presenting papers seems little silly because the chance that everyone in the class will have the background to understand a random paper is slim to none

Of the people in the class, two are numerical analysts, one does nonlocal operators, one does probability

Semiclassical

in doing that, you end up getting a power series $h(x)=a_0 +a_1 x+a_2x^2+\cdots$ where $a_{n}=p(n)a_{n-2}$ and $p(n)$ is some rational function I don't remember

0ßelö7

4:44 AM

I don't think I'd understand any of that

Semiclassical

yeah, that seems like it could b hit or miss

ideally they'd be able to present their topic in a way tat's accessible

buuuut

0ßelö7

Recently I've been interested in Dirac-type elliptic PDE on asymptotically Euclidean manifolds

But that's hardly something I can talk about in an hour

Defining spinors would take an hour alone

Semiclassical

can't help you much there

0ßelö7

@Semiclassical I thought something more appropriate would be a very basic introduction to function spaces on manifolds, but that's not a "paper"

I'll have to ask the prof what he's looking for

I don't particularly care to give a talk and have no one know what's going on

and vice-versa

Semiclassical

yeah, talk to the prof

he presumably knows what kinds of presentation he's looking for and how people have approached it in the past

0ßelö7

4:51 AM

yeah

Semiclassical

that's the same plot as in my question, but with black instead of green in the middle

0ßelö7

what is the black curve?

Semiclassical

$\frac12(W_0(x)+W_{-1}(x))$ where those are the $k=0,-1$ branches of the lambert-w function

0ßelö7

oh, oh

that's the average, got it

So...is this a curiosity or is it really important?

Semiclassical

it was important when I still had it at the forefront of my mind :/

0ßelö7

4:57 AM

it's certainly interesting

@Semiclassical important because...?

Semiclassical

yeah.

research stuff, basically.

that function is my toy model for what a certain paper was doing

0ßelö7

Ok, so the smoothness is important for the physics or for a rigorous result?

Semiclassical

tbh I'm not sure

the paper was really not clear.

mostly I was trying to find a reason why one would think of the black curve as a valid 'continuation' of the blue curve.

and stumbled across that along the way.

(basically: if you were thinking analytic continuation, you'd follow the blue curve up to x=-1/E, and then follow the orange curve as it moved back towards x=0. but for some reason the paper said that the black curve was the right one to follow towards x=0. the fact that it's a smooth continuation of the real part was the best I could come up with, but I couldn't explain why it was smooth.)

0ßelö7

Ah, ok

Semiclassical

the horrible thing is that this is only a toy version of what the paper was doing

but I had managed to convince myself that this was the heart of the matter

0ßelö7

5:09 AM

did you figure out their not-toy model?

Semiclassical

nah, put it on the back burner

0ßelö7

@Semiclassical it's coming along nicely i.gyazo.com/43b7bdc19deea0a0300a95fb04df15eb.png

Anonymous

5:33 AM

@Abcd Neither. Use $\delta Q$ as it is not a perfect differential.

0ßelö7

@Semiclassical thanks for the help on this, I owe you a beer

Semiclassical

np

Balarka Sen

6:25 AM

@Semiclassical Someone sent me this. I am going to read this.

3

It looks very neat.

0ßelö7

@BalarkaSen I cannot contain my horror

Balarka Sen

lol

why are you so mean? it's full of beautiful pictures

0ßelö7

I am a fan of 60s math

Pictures only obscure the mathematical beauty and rigor

I didn't see that!

Balarka Sen

lol

oh well

0ßelö7

Say it again

Wow

I don't think we can be friends after that

Balarka Sen

6:34 AM

lolol

John Rennie

@BalarkaSen from a quick scan through that looks a really nice article

Balarka Sen

@JohnRennie Yeah

John Rennie

A good way for beginners to get a grasp of what is actually going on

Prathyush Poduval

@BalarkaSen is the video the inspiration behind your pink avatar?

Balarka Sen

i should change my avatar back actually

until i find another inspiration

Prathyush Poduval

6:37 AM

i'm sure you have plenty :P

0ßelö7

@JohnRennie what is there to grasp?

What a 2-form is? Who knows

Does it really matter?

Prathyush Poduval

0ßelö7

@JohnRennie don't forget MTW Second Edition is being released in a couple of weeks

Prathyush Poduval

@BalarkaSen How ;bout this?

Balarka Sen

tunak tunak tun woah woah woah

Prathyush Poduval

6:39 AM

tunak tunak tun

Balarka Sen

nah crash bandicoot is a dead meme

some people are trying to revive him but he's dead

John Rennie

@0ßelö7 There's definitely a critical (mental) mass with subjects like diff geo. There's a point below which it all seems mysterious and above which it all makes sense. If a few pictures help students get to that point then I think that's a good thing. Once you've achieved Zen mastery you can forget the pictures of course.

Prathyush Poduval

then i'll take it

0ßelö7

@JohnRennie yeah, but I think Balarka has the best zen mastery around. I don't know what he thinks he can gain from it

John Rennie

@0ßelö7 I suspect he was just pointing it out as a useful guide for beginners, and not as essential reading for his own benefit. @BalarkaSen: comments?

0ßelö7

6:42 AM

Actually after that video I refuse to acknowledge his existence

Gnight

Balarka Sen

I think mathematically I know most of the stuff that's in there but I still want to read it for aestheticc experience

@0ßelö7 lol u mad bro

IT'S JUST A PRANK BRO

►

0ßelö7

I can't hear you

Balarka Sen

But yeah I think the pictorial presentation that's in the paper is very nice for beginners. There's an extra appeal to visual mathematics; eg I myself am curious to read the paper even though I think I "know" the mathematics

In my opinion intuition should be valued far more than formal knowledge

who in the god's nickname is starring everything in sight

Anonymous

What's up with the starring? :D

John Rennie

There's only four of us active ...

Anonymous

6:55 AM

@BalarkaSen That paper seems to be based on topology (?) It looks interesting. But I can't understand most of it :P

Anonymous

I don't know manifolds and stuff

Mithrandir24601

In other news, there's a new series of W1A :)

Balarka Sen

@Blue He explains things, doesn't he?

He starts off with manifolds

Anonymous

@BalarkaSen Oh, just noticed. That's nice. I should give it a try. Perhaps I should even formally learn topology sometime.

John Rennie

@Blue I've only scanned the paper, but it looks a nice way to explain what differential geometry is all about. I'd say it was worth a read if you have a spare hour or so.

Balarka Sen

7:08 AM

True ^

John Rennie

You may or may not decide to subsequently learn it rigorously.

Anonymous

Seems so. Okay, I'll try to read it up this weekend. :)

Anonymous

Bookmarked!

Koolman

Hii @JohnRennie

Space Otter

7:28 AM

In quantum mechanics what is the unit operator?

Anonymous

Bra–ket notation

In quantum mechanics, bra–ket notation is a standard notation for describing quantum states. The notation uses angle brackets ⟨ {\displaystyle \langle } and ⟩ {\displaystyle \rangle } , and vertical bars ∣ {\displaystyle \mid } . It can also be used to denote abstract vectors and linear functionals in mathematics. In such terms, the scalar product, or action of a linear functional on a vector in a complex vector space, is denoted by ⟨ ϕ ...

Space Otter

"If $U$ is the time-developement operator for the system then $U*U$ is equivalent to the unit operator"
What does the unit operator do?

I understand that this is quite basic so I'm just making sure it is what I assume it is

Sorry by $U*$ I mean the hermitian conjugate of $U$, I just didn't know how to make the small dagger symbol

John Rennie

\dagger

Space Otter

$U^\dagger U = I$

What does the unit operator($I$) do?

@JohnRennie Thank you

John Rennie

7:46 AM

The unit operator leaves the wavefunction unchanged i.e. $$\hat{I}|\psi\rangle = |\psi\rangle$$

I suppose formally all wavefunctions are eigenfunctions of the unit operator with eigenvalue $1$.

Slereah

yes

Space Otter

So it really does nothing? @JohnRennie

John Rennie

@SpaceOtter Yes

Space Otter

That's quite useful

@JohnRennie Thank you

I suppose that should be intuitive

considering $U^\dagger U$

Prathyush Poduval

@Blue do you have a real analysis course in college yet?

Anonymous

7:53 AM

@PrathyushPoduval Depends on what you mean by real analysis. We have multivariable calculus, complex analysis, vector calculus, and differential calculus (Calculus 2) this semester.

Balarka Sen

Saying that $U^\dagger U= I$ is the same as saying $U$ is unitary I think

aka it preserves the inner product

Anonymous

@PrathyushPoduval By the way that Arduino book (by Massimo) looks quite short. I could complete half of it in around 3-4 hours. I need to search for a more advanced book now. I'm more or less done with the basics. :)

Anonymous

The next part of the books deals with Arduino Leonardo, humidity sensing, etc

Anonymous

I think I can skip that

Prathyush Poduval

8:19 AM

@Blue Yeah thats what i meant. Which books did you use/

@Blue you can find a lot of cool projects online by just googling it. Maybe you can check then out :+)

Anonymous

I had bought Courant and John, Spiegel, Arumugam(Complex Analysis)....but I'm not using the books much. They seem to be missing lot of things which I need and also have a lot of additional things. I'm mostly studying Calculus stuff from Khan Academy and doing some exercises from those books. Professor Leonard's channel on Youtube is also helpful for Calculus 2.

Anonymous

Khan Academy's multivariable calculus is really really good.

Anonymous

Though they contain mostly theory

Prathyush Poduval

professor leonard.... susskind??

Anonymous

@PrathyushPoduval youtube.com/user/professorleonard57

Prathyush Poduval

8:24 AM

Aah okay :P

Anonymous

These popular books like Spiegel and stuff are really overrated.

Prathyush Poduval

I'm planning on learning differential geometry (of which i now almost nothing), for which I have started learning real analysis

Anonymous

I don't know why year after year teachers tell students to buy those

Prathyush Poduval

ebooks can be used

you seemed to have bought a awful lot of books

Anonymous

@PrathyushPoduval I bought only 3 for maths

Anonymous

8:27 AM

Reading math from ebooks is difficult

Prathyush Poduval

you can buy a tablet (or ipad) and get all your ebooks on it

Anonymous

@PrathyushPoduval ocw.mit.edu/courses/mathematics/…

Prathyush Poduval

yeah ik, but i primarily read everything from my notebook

Anonymous

ocw.mit.edu/courses/mathematics/…

Anonymous

These two look good

Prathyush Poduval

8:28 AM

@Blue Yeah mit courses are quite good

but I'm stuck in real analysis for now

Anonymous

I plan to start with topology and differential geometry next year. This year I'm focusing on Analysis/Calculus and Linear Algebra

Anonymous

We also have those Integral Transforms in syllabus this year

Anonymous

@PrathyushPoduval Same here

Anonymous

I wish Khan Academy added more college math topics :/

Anonymous

They teach really well, with nice illustrations

Anonymous

8:31 AM

I was having a tough time visualizing grad, curl, divergence before that

Mithrandir24601

This is good for diff geometry (the lecture notes we used in my MSc): johnwbarrett.wordpress.com/…

Balarka Sen

Good to see everyone is interested in learning math properly.

John Rennie

I see Susskind has a new Theoretical Minimum book out about relativity.

Mithrandir24601

@BalarkaSen I'm actually going to be tutoring maths (presumably some sort of maths for physics) from January :P

Anonymous

@Mithrandir24601 Tutoring is a good way to keep in touch with topics you studied earlier :) BTW you'll teach undergrads?

Prathyush Poduval

8:33 AM

@Mithrandir24601 Thank very much!

@BalarkaSen What path do you recommend in learning diff geo?

@Mithrandir24601 I'll take a look at that once i'm done with the basics :P

Mithrandir24601

@Blue 1st years, yeah

It's a great way to learn, never mind remember stuff :)

Anonymous

@Mithrandir24601 Nice. Even here, two of our math teachers (for 1st year) are PhD students.

Anonymous

Good luck

Balarka Sen

@Mithrandir24601 Cool!

Prathyush Poduval

@Blue teachers or lecturers?

Balarka Sen

8:36 AM

@PrathyushPoduval Ok, well, first, you need to know multivariable calculus.

Mithrandir24601

@PrathyushPoduval they're for mathematical physics, so from a proper mathematical perspective, they probably are a bit basic :P

Anonymous

@PrathyushPoduval Yup, lecturer

Balarka Sen

That's an absolute gateway to differential anything you want

Prathyush Poduval

@Mithrandir24601 Well, I'm learning it to progress ahead in physics :P

but i don't want to take the intuitive approach

Anonymous

@PrathyushPoduval What?

Prathyush Poduval

8:38 AM

seeing as I have to anyways take a math rigorous course in college

Anonymous

Math without an intuitive approach seems lifeless to me... :P

Prathyush Poduval

I meant it in the sense that you do everything properly

Anonymous

Oh, that's fine

Balarka Sen

@Blue But always thinking intuitively renders a person unable to do any proper mathematics.

Prathyush Poduval

While doing physics, many math concepts were like "It feels correct, so should be correct"

Mithrandir24601

8:40 AM

@PrathyushPoduval I'm going to agree with @Blue here and mention that this is maybe not the best way, at least for me for diff geometry

Balarka Sen

Learning the formal language of mathematics is an essential part of mathematics. Handwaving is just bullshitting, not mathematics.

Prathyush Poduval

^exactly

Balarka Sen

I encourage intuition-based learning, but you need to know how to translate intuition into proper math.

Probably a lot of physicists would disagree with me but that's fine

Anonymous

@BalarkaSen I didn't mean that. I mean directly jumping to abstraction is not something I like, I like to develop intuition first and then translate to abstraction. For example I always do stuff in R^2 or R^3 first and then try to generalize it

Prathyush Poduval

@Mithrandir24601 well, even i cannot do maths without intuition. So far I've been able to convert my intuition into rigorous proofs

Mithrandir24601

8:42 AM

As in, I would learn non-rigourous ideas like co-ordinate transforms, vectors etc. Before going fully differential geometry

Anonymous

Perhaps that's because I'm more of an applied guy

Balarka Sen

@Blue That's ok

@Mithrandir24601 Eh, the two things you mentioned are not non-rigorous ideas.

But yeah one should know linear algebra before differential geometry.

Prathyush Poduval

@Blue Yeah that's what I meant by rigorous, use intuition, but don't use it

in your proofs and defenitions

Mithrandir24601

@Blue yes, this exactly. This is also usually much more relevant for a lot of physics, which feels less rigourous in things like this precisely because there are a lot of assumptions about the space already in play

Balarka Sen

My personal philosophy is whatever approach you take to understand math is fine as long as you can actually compute stuff

If you can't do calculations, you know you are not really learning

John Rennie

8:47 AM

That is such a naff avatar :-)

Prathyush Poduval

@BalarkaSen What kind of calculations come up in maths? o_O

Mithrandir24601

@BalarkaSen as in, I never really had a 'rigourous' idea of what e.g. a vector space is before dg, but I did have an intuitive idea, which made learning the rigourous one so much easier

Balarka Sen

@Mithrandir24601 I see. I do suspect the physical point of view (the glasses through which I don't usually look at the mathematical world) is useful for understanding a lot of geometry.

@PrathyushPoduval Eh, pretty much literally whatever kind. Math is not really spewing handwavish theories and abstractions, contrary to popular belief; you have to get your hands dirty by doing actual, hands-on calculations to get used to mathematics.

Mithrandir24601

@BalarkaSen yeah, very much so x100

Prathyush Poduval

@BalarkaSen thats what i thought maths was :P

@Mithrandir24601 do you get paid for tutoring, or is it voluntary?

Balarka Sen

8:58 AM

@PrathyushPoduval the impression high school gives of math is, you have this and this and this brand new concepts (say when calculus is introduced) and do this and this and this problem which are a bunch of unmotivated exercises

that's not how it works

a surprising amount of math is similar to natural science in the way that there is experimentation, observation and conclusion/explanation involved

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