@yuggib $G/\ker\phi\cong\operatorname{im}\phi$?

@yuggib is ^ true for all groups

Lee proves it for Lie groups and it needs quite a bit of machinery

it assumes something on $\phi$?

just that's its a Lie homomorphism

I would say that it is true in general

with a group homomorphism

but I'm not sure

I think "Lie group homo" means it's a homo and also smooth

a smooth homo :^)

yeah...but for general groups you do not need a notion of smoothness I would say

still the result seems plausible

hmm, what is a Lie group isomorphism

is that an isomorphism that is also smooth?

ah, Lie isomorphism = Lie homomorphism + diff

isomorphism is more than homomorphism

iso is a bijective hom

not all hom are iso, but all iso are hom

I know basic terminology...

I'm telling you what a Lie group isomorphism is

it's a Lie group homomorphism that is also a diffeomorphism

so $\phi$ is a lie group homomorphism and then $\tilde \phi:G/\ker\phi\to\operatorname{im}\phi$ is a Lie group isomorphism

@yuggib are there alternative symbols for $\ker$ and $\mathrm{im}$

@0celo7: the result for Lie groups is diffeo instead of iso?

and hence harder?

@Huy maybe

@0celo7 in place of $\mathrm{im}$ you could use $\mathrm{Ran}$ but it's probably more analysis oriented

doesn't seem like it should be much harder than the purely algebraic result

but maybe I'm wrong

haven't tried it

@Huy he uses some facts about submersed manifolds

let me think about why you need submersions

@yuggib ok have you figured out a payment plan

@Huy because quotient groups are submersions?

and then he applies inverse function thm?

ok he also proves the general algebraic theorem

@0celo7 that does not sound easy...

or not, lol

the proof is an exercise

It would be easier that you give me like a paypal account or something to pay the book with :-D

@yuggib or if you give me yours and I send you the money

ah ok

let the frustration begin - grading my students' tests now

@0celo7 give me the link to the book

I want to see how the payment goes

@yuggib don't you have uni account?

@yuggib I'd only save like 15 bucks

it's not a big deal

it was your idea :-P

ams.org/bookstore-getitem/item=GSM-107

also if you want to get me Evans PDE book

I could use that next semester

@yuggib have you used Evans

@0celo7 yeah, I know it

it's the standard reference for linear PDEs

I have to make the order directly with the credit card

it's too difficult

you should probably pay the $47 for the AMS student membership and then enjoy the discounts

:-P

when are you leaving Sgart

@yuggib perhaps!

in two days

ok

if else it would have been easier

yes you could have stolen a blackboard and taught me some math :P

@yuggib some PhD level set theory theorems

i.e. that the reals are uncountable

that they cannot be well ordered

wow 3 ppl gun cry when they get their tests back

pik?

u wan c piks of previous tests?

I know you have an iphone just post the piks here

no the shitty ones

idk sometimes I don't get it

like really easy problems

where everything is uniformly distributed

they can't solve

show!

and then there's exercises where they have to apply Bayes

and that they can do

makes no sense

dude which ones is Bayes

swap order of conditional probs

like $P(A|B)$ shit

ye

I knew that when i was taking probability

I had a mathfails folder somewhere on my HDD

I'll search it later

just finished with the easy warmup problems

and you know they're gonna cry already?

yes

0 points in 5/10 problems

although these people would cry if they miss one problem

not gud

@Huy holy shit

I once had a kid who had 2 points out of 30 two years ago

he couldn't even compute a scalar product of two vectors in R^3

I couldn't either

what was the metric?

:(

Euclidean

without that you can't do shit

oh that's easy :/

he dumm

yup

@0celo7 ahaha exactly ;-)

it's just $v_1v_2\cos\theta$

at his HS graduation exam the teacher (I was just sub) asked him how many solutions a cubic equation in general has

where you get $\theta$ with your geo-dreieck

@0celo7 first one is true, the second false (if you have the axiom of choice)

or whatever the fuck the english word is

he didn't know, so the teacher asked him to solve a system of 2 linear equations with 2 variables

and he couldn't do it either

so the teacher asked him to solve a linear equation with 1 variable

that he managed to do

Hey guys. I'm doing an finals project on exoplanets and I have to write about rocket equations. Does any of you know a good place to find information and learn about that?

@Huy 1real 2 complex conjugate or 3 real

very good

^.^

did not learn that in high school

did I send you the vector geometry exam I wrote

but when learning complex calculus I proved the fund algebra theorem

1.5 years ago?

I could not do it.

@Huy hmm, that's not hard

yes, it isn't

just invert the matrix of coefficients

or do GJ elimination

but the hard one they can

the best part is the easy Bayes question they can't answer

what is it

well the easy one is the typical one

lemme take a crack

where you have some illness for example 100 out of 1.1 million people suffer from. then you have a method to test it, and the method doesn't recognize the illness in 0.01% of all cases whereas it gives you a false positive in 0.1% of all cases. now you do the test and it is positive. what's the probability that you suffer from the illness?

that's like the most typical Bayes application

that one was on a test but with breast cancer

yea

@Huy Not gonna do it.

np don't expect you to

@Huy NB: I got it right

NB?

nota bene

man I have to teach stat after xmas

I'd much rather skip it and just do diff eqs and complex numbers

when I paid attention to probability I knew how to do that...ask me again when I'm taking the proof based prob class

probably semester after next

@0celo7 what is a proof based class?

measure theory

@yuggib not for engineers

@Huy no

@0celo7 k

how else do you do proof based probability if not with measures

@Huy dunno, but there is that probability as well

kolmogorov's classical probability?

how the fuck would I know?

I haven't talked to the prof.

how the fuck does kolmogorov do it without measures?

probably also kolmogorov's one has measures

we did kolmogorov with measures

I just know that my advisor told me to get out the one that I would be taking, math majors shouldn't take it.

checked the original book, and it seems that up to expectations (excluded) you could avoid measures (however that is quite expected)

@0celo7 why don't you take measure theory then? You will need it in many places

@yuggib who said I won't

can't take measure theory before analysis

@0celo7 pretty sure you could

@yuggib how about no

measure theory is taught in the grad level analysis class

@0celo7 it is more important to know topology than analysis to do measure theory

why

@yuggib and undergrad real analysis does a lot of topology

but I think we've been over this before

analysis is a prereq for all math classes past a certain point

it's the department's notion of "maturity"

link.springer.com/book/10.1007%2F978-1-4684-9440-2

@yuggib not on campus

if you take a peek at the prerequisites (they should be free)

you see that not much analysis is needed

@yuggib dude I don't have time to take 7 math classes at once

@0celo7 so essentially having taken analysis is an excuse to be sure that you know some mathematics

@yuggib to keep engineers out of the higher math classes

@0celo7 because you are weak :-P

@yuggib no because I'm a double major

@yuggib liar

if you look inside?

I get the first page?

it's one page in total...

the part on the prerequisites

clicked on the wrong chapter lol

well I'll get most of those things in analysis

or...all of them

but probably you already know them

nope

name me one that in all honesty you do not know

I know (1)

the others I don't know

maybe (4), that's kinda vague

you don't know (3)??? I don't believe you

I know it

I can't prove any of those statements

I can't prove 99% of what I say

that does not mean you do not know they hold true, or what do they mean

and why would you not believe me

wanting to prove everything is admirable

should a second semester student know all of these things

I would say yes, because most of them, if slightly rephrased, you know from high school

oh I forgot you're from a country with smart people in high school

we don't learn any of that in high school

you don't learn limits in high-school?

define "limit"

in the sense of the real line

epsilon-delta definition

nope

o.O

that's not good

I guarantee none of the teachers know it either

I can

that I could not believe

@yuggib believe whatever you want

I'm telling you the way it is

T__T

math teachers are not the good students

I keep telling people this

yes, also here it is the same

they're the people who could not get into grad school

in many cases

to teach calculus in my district

but still they know that a limit is defined by epsilon-delta

you needed a BS

that's it

no, in my country you need also a MS

not here

or if you do, then they'll take one in education

or "math education" or whatever

ok, but again every math BS holder knows the definition of a limit in the real line

@yuggib lol

at least in europe

not a math BS

some BS

@_@

we have math teachers with PhDs

my dad's an engineer and taught calculus

also in fine arts?

yes there are people with art degrees who have a Bachelor of Science

like 4 at my school

@0celo7 that's borderline reasonable

very good acronym analysis @yuggib

@yuggib when I told him about epsilon delta

"what's this useless crap"

"just take the limit"

@0celo7 I don't know the educational system of the US

@yuggib BS vs. BA

you guess which ones is art and which is science

the PhD stands always for philosophiae doctor

people like my dad will specify "technical PhD" or "liberal arts PhD"

because some dirty english doctor could claim to be decent without that distinction

@0celo7 ok, so you categorize philosophy, language studies under arts?

yes

they're useless degrees, right?

that's probably true, but philosophy is almost as far from art as mathematics

but ok I understand, we group them under "humanities"

@yuggib yes

now, he don't know what to do about Psychology

just to understand it better: in the wikipedia page it says that e.g. Georgetown's Foreign Service students get a B.Sc.

so they could teach math??

I would be scared to send my kid to an HS where math is taught by a foreign affairs graduate

@0celo7 Psychology is definitely humanities

@yuggib wtf is the foreign service

@yuggib maybe...

@yuggib well the math department would reject them!

but you get the idea...

one year our school had a biology teacher teaching calculus

my physics teacher was probably the best qualified to teach calculus...she's a EE

took analysis and all that jazz at Princeton

@Huy how did the pedagogy exam go

was fine

much harder than you expected, right?

failed

poor you

the good part was that there was a possibility for an evaluation after the exam

where you could rate things from the course on a scale from 1 to 10

I gave 20x 1

even with comments

holy shit a 20??

so they know I'm not just a trol

must have been a great course

very

@Huy any word on (3)?

wtf is a dyadic expansion

yeah the worst student got 1.5 out of 27 points

no idea what she was doing

she was doing well during class

that would be me

I could probably not do better than that

freaking MS level probability I bet

poor gril

there were two who were quite good

they would complement each other well

one girl did all the easy to moderate exercises perfectly

and one guy did all moderate to hard exercises perfectly

@yuggib I might want to read some diff top before I read that geo book

@Huy lol

you should write that on the papers

wat

freaking pimp...

hue

huh, I don't think $S^4$ has a Lorentz metric

the universe cannot be $S^4$ o.o

crazy

@Huy can you check for me pls if Hirsch diff top is available for mycopy purchase

@0celo7 yeah...it's always about having the right prerequisites

no

the exam was actually not as bad as I thought it would be when correcting

a bit worse than usually

but yeah this one girl gun cry

:(

@0celo7: i.imgur.com/ZjbXUpo.jpg this is probably the classic "joke mistake"

except it wasn't a joke

that does not surprise me...

a really really good one:

we did the binomial theorem

so one problem of the exam was to compute $$\sum_{k=0}^{13} \binom{13}{k} 2^{13-k} (-3)^k$$

so there was only one student who correctly identified this sum as $(2-3)^{13}$

guess what he did next

wow...well I personally heard a guy that in the final exam of the analysis one course for physicists asserted that $\lvert x\rvert <-1$

nice

and when the mistake was pointed out he obviously made the correction $\lvert x \rvert \leq -1$

:-D

@ACuriousMind : The Cameron-Barnett paper also uses eom (3.8) in the Noether argument from eq. (4.2) to (4.3). That is not correct.

@Qmechanic I think it is for what they are doing - (4.3) is meant to be the expression that gives conservation of the Noether current on - shell, I think

It's bad style to write, $\Delta L$ for that, though

@0celo7 That's correct. The same argument actually shows that it can't be any simply connected closed 4-manifold.

@Huy holy shit

@MikeMiller yes

@ACuriousMind Does it? funny.

@ACuriousMind Went to a Czech Weihnachtsmarkt

I recall an exercise in my Riemannian geometry course where we related it to the hairy ball theorem, too (I guess that's kind of the same thing in some sense)

Had some Gluhwein with honey

Also pig knee stew or something...that was interesting

don't know what you're talking about

> The Committee which was set up in Rome for the unification of vector notation did not have the slightest success, which was only to have been expected.

Interesting quote from Klein

@0celo7 That sounds interesting. Link?

@Danu Hirsch, Differential Topology. 19something, Springer. Page 85.

Author-Title is sufficient :)

@Danu wanted to be official

By the way @MikeMiller is "tubular neighborhoods" a standard topic for a (full year) course on algebraic topology?

It's not really an algebraic topology topic, since it's about manifolds. But it's a standard topic in any manifolds course.

@MikeMiller Really? Does e.g. Lee even mention them?

Sigh... I took a one-year sequence of diff. geom. and did not hear about them :(

I think Lee does them, yes.

I'm sure he does.

I should say "any manifolds course that mentions vector bundles", since the correct statement is that there's a neighborhood diffeomorphic to the normal bundle.

Ah, yes. In the chapter I haven't bothered with.

In the chapter on whitney

@MikeMiller Half of that sequence was devoted to Chern-Weil theory...

Nonstandard treatment yaaaay :(