Mathematics - 2017-09-15 (page 7 of 7)

Dodsy

11:00 PM

That's awesome Ted.

Faust

@KasmirKhaan aH left Ha right coset

Ted Shifrin

It was a lot of administrative work, Nate. But someone had to do it. I taught a bit less, but still more than most people in that position.

Kasmir Khaan

@Faust thanks, it is a bit odd because H is in the wrong side =p

Faust

its about the element a not H =)

Kasmir Khaan

:)

Daminark

11:01 PM

@Ted how much did you usually teach?

Dodsy

@TedShifrin imgur.com/a/vniQK

Faust

@TedShifrin did you take less grad students because of it?

lol Dodsy

Ted Shifrin

Demonark: I normally taught the equivalent of 5 3-hour classes, whereas most research-active faculty did 3 1/2. (Calculus counted as 1 1/3 because of the fourth hour.)

Faust: I only had one grad student in my whole career. I was more into working with undergrads.

Faust

wow

Dodsy

3 hour classes would be awesome.

I have 1 hour classes and I always leave wanting more.

Faust

11:04 PM

i had a 3hr biology class once a week could never stay awake for all of it

Ted Shifrin

No, no, 3 1-hour classes.

A 3 credit course.

Daminark

I think it's 3 hours per week

Sniped again...

Dodsy

:(

Ted Shifrin

Yeah, literature with discussions works for one 3-hour meeting, but I taught very few math classes (diff geo and some grad courses) where we met 1 1/4 hours each session.

Kasmir Khaan

if we have a map in general, and we found it inverse

Faust

11:05 PM

most of my classes are 1.5hrs twice a week

Kasmir Khaan

does this tell us that the map is bijective?

Faust

no

consider the map on the natural numbers

Kasmir Khaan

why did my teacher use that as an argument then grrr

Faust

where f takes 1 to 2 and 2 to 3 etc

Ted Shifrin

What's domain and range?

Dodsy

11:06 PM

@TedShifrin I bet next year I'll feel differently when I have more math courses/am full time.

Faust

consider g that takes 1 to 1 and 2 to 1 and 3 to 2 etc

Kasmir Khaan

aH --> bH , ah---> bh where h in H

the map from aH to bH is multiplication by ba'

Ted Shifrin

That is obviously a bijection.

Faust

g is a right inverse of f but neighier are a bijection into the naturals

Kasmir Khaan

the other way around is ab'

Ted Shifrin

11:07 PM

Too many conversations happening.

Kasmir Khaan

@TedShifrin why you say avious?

@Faust you took an infinite case =p

Dodsy

@Daminark hows the start of your term going?

Daminark

Class is starting for me in about 10 days

Luke

Hey, from the top of your head, what are usual ways to prove two subgroups intersect as ${e}$ if you've defined them as a normal closure? E.g. in the rubik's cube group, you generate subgroups by certain moves and use them to describe the group as a semidirect product, but I didn't see proofs of that.

Daminark

I'm still actually trying to figure out my last class

Ted Shifrin

11:09 PM

@Kasmir: Even if $H$ is infinite, it's obviously a bijection.

Faust

you can have infinite cosets but that still never happens :p

dam you Ted

Ted Shifrin

<--- should just shut up

Faust

lol

Daminark

Ted's just gunning us down

:P

Kasmir Khaan

Erhmm Ted is awesome thats y :D

Daminark

11:10 PM

@Dodsy how's it going on your side?

Kasmir Khaan

Okay guys i think I got it =p thanks

Dodsy

@Daminark 10 days!? that's crazy. And pretty good. I'm really enjoying calculus and my teacher is really great. But physics seems slow atm, and it turns out that it is not going to be calc based this term. And then lin alg is a massive mess. So we'll see how it goes. I love calc though.

Faust

@TedShifrin Suppose that G is a cyclic group of even order. How do i prove that G has only one element of order 2?

Ted Shifrin

Write down what the group is.

Dodsy

But my physics teacher said something silly today about finding the instantaneous velocity being difficult due to calculus, and also didn't recognise that you can get a very good approximation using the secant method.

Faust

11:13 PM

i need to prove it for any cyclic group with even order

Ted Shifrin

difficult due to calculus?

Faust

but i guess $ Z_4$ with addition works the element of order 2 is the number 2

i feel like im missing something critical in my understanding of groups cause i keep thinking why not two elements of order 2

Ted Shifrin

Try $\Bbb Z_{2n}$.

Dodsy

@TedShifrin yeah really weird...

Faust

well the element n will always have order 2

Dodsy

11:15 PM

He said that calculus was messy and said we're just going to use "the big four" kinematic equations.

Ted Shifrin

@Faust: Could there be another?

Dodsy

there's a few other things he says / does that just seem off.

Ted Shifrin

Ugh ... physics without calculus is just memorized formulas.

Dodsy

and he said we won't do integrals and will just assume that acceleration is always constant.

Yeah exactly.

Faust

@TedShifrin well no

now i sound crazy =P

Ted Shifrin

11:16 PM

Now write a proof.

Faust

well everything smaller than n will need more than two steps to get to 2n

Dodsy

Let x be my broken dreams- like that? @TedShifrin

Ted Shifrin

Hush, Nate.

Faust

and everything bigger will go over 2n in two steps

thats not a proof but its my logic into why

Dodsy

:P

Jasper

11:18 PM

@Dodsy I think he is just saying that the course doesn't assume knowledge of calculus, so you will be doing the simplified version of everything.

Dodsy

Yeah and that's what I hate.

Faust

@Jasper Sup old man >.>

Dodsy

I signed up for the "enriched" physics course for a reason.

Ted Shifrin

You can make that a solid proof very easily, @Faust. I dunno if you want to use additive or multiplicative notation for the group.

Jasper

@Faust LOL. Nothing's up. Everything's down for me. =(

Dodsy

11:19 PM

cheer up buttercup @Jasper

I did happen to walk by a gentleman on the phone (presumably to his mother) explaining that his classes were too easy and "beneath him"

Faust

@TedShifrin yeah i think ive actually done the proof before thanks =)

Jasper

@Dodsy The other simplification is doing things in 1 dimension instead of 3. When the switch is made, some get confused.

@Dodsy I believe that sometimes not simplifying things makes things clearer, for example, using vectors in 3 dimensions instead of making one direction positive and the other direction negative when doing motion in 1 dimension.

Faust

@Jasper i noticed you pulled the trigger on the mse boom boom button yet again

Dodsy

Yeah, it should be fine. I'll just focus on getting a good grade.

Jasper

@Faust Yes, lol. How's your studies going?

@Dodsy Yeah, just try to get a perfect GPA for starters.

Dodsy

11:22 PM

haha when pigs fly!

Faust

I have 5 classes its a bit long but i got all my assignments basically done just need to rewrite out a couple good copies so i have the weekend to study w.e i want.

Ted Shifrin

Oh yeah. It's the weekend.

Jasper

You know, I used to be really interested in physics, but not anymore. There's too much math to learn already, so I can't be bothered with physics now, lol.

Dodsy

@TedShifrin yes, Ted.

Faust

@TedShifrin your permanently on weekend

Ted Shifrin

11:24 PM

Well, no. Remember I now work on Sundays. :P

Plus you guys make me work.

Jasper

@TedShifrin You are on permanent vacation, lol.

Dodsy

@Jasper I took it because at another school here in Canada, it's recommended for an honours specialization, to take a first year course in physics. So I figured I'd take it and if anything it'd give me some basis for decision on applied math vs pure math or whatever.

Faust

@TedShifrin just trying to prevent you from getting dementia cause we care Ted.

Ted Shifrin

Ha ha, Faust.

Faust

O.o

Dodsy

11:25 PM

one guy said medical physics.

There's people here in first year general science telling people they're majoring in astrophysics. O_O

Jasper

@Dodsy Yeah, it's good to at least do some mechanics. It's actually done in a lot of math courses in the UK.

Ted Shifrin

OK, I have dinner to prepare for company coming later. Bye, all. Have a good evening/weekend.

Dodsy

bye Ted.

Faust

thanks ted

@Dodsy just try not to get too distracted if its your first year at uni

Dodsy

Ofc not.

I can't afford to drink away from home anymore

and too old to fraternise

Jasper

11:26 PM

@Semiclassical Your avatar is kind of weird because of the colour and the pattern. It must be very strange that you got that one, lol.

Semiclassical

eh, so it goes

i'm too lazy to get another

Dodsy

I like it, Semi.

Semiclassical

heh

Faust

i wouldnt mind a fracal pattern

Semiclassical

@Dodsy What've you got as the 'big 4' of kinematics?

Dodsy

11:27 PM

Haven't started yet :(

Jasper

@Dodsy Why did you use an old man for your pic, lol

Dodsy

I assume that it's going to be high school physics all over again semi.

Semiclassical

In physics the way I like to describe kinematics is "a machine we use to turn information about the system at one time into information at another time"

Dodsy

but I feel like for physics and linear algebra, I could've saved 1500 dollars and read the textbook instead of going to school.

2

Semiclassical

tbh, I think physics doesn't really start until you get to forces

before that it's really just consequences of how motion etc is defined

Dodsy

11:29 PM

But then, calculus is crazy. The teacher knows his content so much and basically just forces us to read the textbook. He wants us to sleep with it under our pillow, but doesn't even teach from it (for the most part) he basically uses the readings as a foundation for whatever else he's teaching us.

I love calculus.

at least that's my opinion on what is happening in that class.

Semiclassical

re: the big 4, I mostly wonder b/c here one talks about the big 3

Faust

Calculus is a very intresting subject

2

Dodsy

:o

I keep timing out.

Semiclassical

$x_f=x_i+v_i t+\frac12 a t^2$,
$v_f=v_i+at$,
$v_f^2=v_f^2+2a(x_f-x_i)$.

Faust

@Semiclassical one of them ate the other?

Semiclassical

11:31 PM

?

oh

Dodsy

Back.

Faust

whats $f^2$4

nvm

Semiclassical

though I also really don't like including the third one

Dodsy

So I didn't write down exactly what he said, perhaps he said 3.

Faust

that looks more familair

Semiclassical

11:32 PM

The first two are immediate consequences of "acceleration is constant"---just take antiderivatives w/r/t time

user228700

Hi, everyone :-) Can anybody help me with some multivariable calculus?

Faust

maybe

Dodsy

Today in calculus teacher asked what the range of $f(x)=\sqrt{3x-9}+\sqrt{4-(x-4)^2}$ was and it ended up being complicated.

Semiclassical

the last one is what you get when you eliminate $t$ from the first two. Or, at least, that's how you obtain it in the context of elementary kinematics

hrm, I can imagine.

user228700

Specifically, with Clairaut's Theorem of Equality of Mixed Partials.

user228700

11:34 PM

Mine is a simple question, really. The theorem itself is stated using slightly different words in my textbook and I was wondering if anybody could please help me to parse it.

Faust

never seen it called that before but its familiar

Semiclassical

the reason I object to calling it one of the big 3 is two-fold. one is what I just said: it's a derived result, so treating it as fundamental seems silly.

user228700

In my textbook, it states "If $f_{xy}$ and $f_{yx}$ are continuous on some open disk, then $f_{xy}=f_{yx}$ on that disk."

Dodsy

hm.

I think I need to restart my computer

Semiclassical

the second is that, on the other hand, it anticipates energy conservation. so later on there's very good reasons why that equation should show up

but putting it in as one of the big 3 separates it from that.

user228700

11:36 PM

What is this disk business of which they speak?

user228700

@Semiclassical Oops! Edited it, thanks :-)

Semiclassical

np

Disk (mathematics)

In geometry, a disk (also spelled disc) is the region in a plane bounded by a circle. A disk is said to be closed if it contains the circle that constitutes its boundary, and open if it does not. == Formulas == In Cartesian coordinates, the open disk of center ( a , b ) {\displaystyle (a,b)} and radius R is given by the formula D = { ( x , y ) ∈ R 2...

user228700

Oh, no, no, haha, I do know the definition of a disk!

Semiclassical

I dunno what you're wondering about, then :/

Dodsy

I am back

@Semiclassical so I wrote my assignment for calc in LaTeX

:o

Semiclassical

11:38 PM

@Dodsy The above said, there is some nice calculus to be had in relation to the equation I don't like

oh, nice

Dodsy

well he suggested it but when he asked if anyone had used it, I didn't put up my hand.

I use it here, but i don't feel like i've really "used" it.

Semiclassical

yeah, there's different levels of latex usage

Faust

@Kaumudi.H normally you define a portion of the real line where something is continous on the real line, in $R^2$ or two variabels you define an open disc of a point

Semiclassical

some definitions: $v=\dfrac{dx}{dt},$ $a=\dfrac{dv}{dt}$

Faust

in $R^3$ you define a sphereical ball

Dodsy

11:40 PM

for sure.

user228700

Oops, I'm sorry about that, my connection suddenly died for a bit there.

Dodsy

My messages are taking too long to send and keep timing out.

Semiclassical

not anything surprising there. what is a bit less famliar is this:

Lucas Henrique

yo.

Semiclassical

From the chain rule, we have $a=\dfrac{dv}{dt}=\dfrac{dv}{dx}\dfrac{dx}{dt}=\dfrac{dv}{dx}v$

user228700

11:42 PM

@Faust Ah, hmm, we define a portion of space one dimension lesser than the graph of the function?

Dodsy

@Semiclassical this looks familiar.

Faust

in calculus of one variable something isnt continous just cause it exists a point it has to exist on both sides of it

Semiclassical

And the last term can be written as $\frac{1}{2}\frac{d}{dx}v^2$.

Dodsy

Learned it today I believe.

Faust

in two variables that range of freedoms means you need a open disc to say anyhting meaniful about the continuity

Dodsy

11:43 PM

@Semiclassical then there's $\frac{d^2t}{dx^2}$

user228700

AH, right, of course! I understand!

Semiclassical

If I move the 2 over, that's $2a=\frac{d}{dx}v^2$

user228700

@Faust: Thanks so much :-)

Faust

np

Dodsy

oh am I confused?

are we talking about physics or....

Semiclassical

11:44 PM

Or calculus? Both, really.

Dodsy

is the chat all messed up atm?

Semiclassical

not for me

Faust

@Dodsy im not sure i know the difference between physics and calculus at least i couldnt define it.

Simply Beautiful Art

@Dodsy messed up in what sense?

Dodsy

I can't send a message without waiting

and there's usually a chance of timeout.

Semiclassical

11:46 PM

Now, suppose $a$ is constant in time. Then it's also constant in $x$, so if I integrate both sides from $x=x_i$ to $x=f_f$ this becomes $2a(x_f-x_i)=v_f^2-v_i^2$---aka just the equation I wrote above.

Faust

@Dodsy did you get into my secret stash of D RUGS >)!@#

Semiclassical

@Dodsy hrm, something wrong with your connection maybe?

Dodsy

@Semiclassical I was more asking if my $\frac{d^2t}{dx^2}$ applied to our conversation or if you were talking to kaumudi. H.

Semiclassical

@Faust when it comes to kinematics, I'd argue there really isn't one.

ah

Faust

@Semiclassical glad im not the only one confused on the difference =)

Semiclassical

11:47 PM

not sure where you're getting that from, though. that'd be $\dfrac{d^2 t}{dx^2}=\dfrac{d}{dx}\dfrac{dt}{dx}=\dfrac{d}{dx}\dfrac{1}{v}$

Dodsy

weird.

Faust

what

Semiclassical

so I'm not seeing how you're getting $\frac{d^2 t}{dx^2}$ in this context

Dodsy

which problem?

oh

my teacher told us this equation today

Faust

@Semiclassical thats notation for the second derivative of time with respect to x isnt it?

it simple = acceleration

Semiclassical

11:49 PM

no.

Faust

oh

nvm

sure it wasnt the opposite @Dodsy

Semiclassical

acceleration = second derivative of x with respect to time

$a=\frac{d^2 x}{dt^2}$

Jasper

displacement, velocity, acceleration, jerk, etc.

Dodsy

$a=\frac{dv}{dt}=\frac{d}{dt}(\frac{dx}{dt})=\frac{d^2x}{dt^2}$

Semiclassical

yep

Dodsy

11:50 PM

for acceleration

Semiclassical

you wrote $\frac{d^2 t}{dx^2}$

Dodsy

I made a mistake

haha

I didn't realize until I typed it from my notes :3

Faust

i didnt even notice till semi pointed it out

Semiclassical

yeah, I was wondering where you were getting that from :)

Dodsy

hey, I was pretty close for being from memory!

Jasper

11:51 PM

I just had spinach and sausage, nice combo.

Dodsy

and having drank 6 beers.

Jasper that's literally horrifying.

Faust

w8 were they real beer or merican beer?

Semiclassical

@Jasper reminds me of the omelet I like to get: cheese, bacon, and broccoli

3

Jasper

Spinach makes PopEye the sailorman strong, lol.

Dodsy

@Faust Becks :o

Faust

11:52 PM

cause i could drink $\lim_{n \to \infty} e^n $ of merican beers and not get drunk

Jasper

@Dodsy How did you drink so many beers? lol I can't even drink one.

Dodsy

true, light beers do nothing to me

@Jasper oh, I'm a degenerate. Didn't you know?

Jasper

Honestly I hate alcohol

Its taste is terrible

Semiclassical

actually, what I think is surprisingly awesome: roasted broccoli

Faust

i sat down with some friends while camping for the long weekend drank a 26er in under an hour the four of them barely finished the other 26er one of them got so drunk they puked and i was still the least drunk of the five of us.

Jasper

11:54 PM

@Dodsy The empty set and the singleton are the degenerate intervals on the real line, lol.

Semiclassical

@Faust I've never understood the appeal of "drink till you puke"

I can understand drinking to get a buzz and to make oneself less inhibited etc

Faust

@Semiclassical he only had like 4 oz's but hes alittle tiny asian guy and got super sick idk how

Semiclassical

ah.

yeah, that's more understandable.

Faust