Mathematics - 2013-03-29 (page 1 of 3)

κρανίοπεριπολία

12:00 AM

Yummy :-D

thanx

Jonas Teuwen

12:14 AM

Congrats. I go to bed.

κρανίοπεριπολία

later

Alexander Gruber

anybody know any good 2nd isomorphism theorem problems?

Alex Youcis

which are you defining to be second?

HN/H=H/(H\cap N)?

Peter Tamaroff

12:29 AM

@AlexYoucis Good question.

I am trying to determine $\langle \alpha,\beta\rangle$ where $$\alpha=\left(\begin{matrix} 0& 1\\-1&0\end{matrix}\right)$$
$$\beta=\left(\begin{matrix} 0& 1\\-1&-1\end{matrix}\right)$$

Note $\beta^3=\alpha^4=1$

But $\alpha\beta$ has infinite order.

since $$\alpha\beta =\left(\begin{matrix} 1& 1\\0&1\end{matrix}\right)$$ so $(\alpha\beta)^n =\left(\begin{matrix} 1&n\\0&1\end{matrix}\right)$

Also $\alpha,\beta\in {\rm SL}(2,\Bbb Z)$

@AlexanderGruber So?

What do you call the 2nd iso. thm.?

Alexander Gruber

@AlexYoucis @PeterTamaroff $2^\text{nd}$ one for me is $HK/K\cong H/(H\cap K)$.

Peter Tamaroff

@AlexanderGruber You missed an $H$ up there.

Alexander Gruber

yeah :P

just realized that

Peter Tamaroff

@AlexanderGruber I liked how Jacobson used it to prove: Let $G$ be a group, $S$ a $p$-Sylow subgroup. If $H$ is a $p$-group with $H\subset N(S)$ then $H\subseteq S$.

How dangerous can a sugar overdose be?

user19161

12:46 AM

@PeterTamaroff A or B is logically equivalent to not A implies B. Just draw a truth table to verify.

Peter Tamaroff

@JasperLoy What about "xor"?

Or is that the one you mean?

user19161

@PeterTamaroff I don't know what xor is.

Peter Tamaroff

@JasperLoy Exclusive or.

A or B, BUT NOT BOTH.

user19161

In math, or is always used in the inclusive sense.

user19161

Unless otherwise stated.

Peter Tamaroff

12:47 AM

@JasperLoy Well, that's why the author wrote either $A$ or $B$.

user19161

@PeterTamaroff Either doesn't add anything to the meaning actually, as far as I am concerned.

Peter Tamaroff

@JasperLoy I didn't know that. I thought it meant exclusive or. =/

Good.

user19161

Sure, some layman will say either adds the exclusivity to it, but I don't subscribe to that linguistic theory.

user19161

OK I just did 5 edits on my own old posts, let's hope that same guy does not complain again.

Peter Tamaroff

@JasperLoy OK. The author wrote this:

Let z be an element of a ring for which there exists w≠0 such that zwz=0. Show that z is either a left zero divisor or a right zero divisor."

user19161

12:50 AM

I am hoping for this to be my final round of edits, which will take a few days to complete since I have 400 posts to look through...

user19161

@PeterTamaroff I interpret that the same way with or without the either, that is, in the inclusive sense.

Peter Tamaroff

@JasperLoy Yes, now I see.

Alexander Gruber

@JasperLoy what are you editing?

user19161

@PeterTamaroff If I wanted to be exclusive, I would manually add but not both.

Peter Tamaroff

Because the proof assuming it means just "or" went swimmingly well.

user19161

12:52 AM

@AlexanderGruber Just trying to format my old posts into better shape.

Peter Tamaroff

What an awesome word "swimmingly" is.

People should know about it.

Alexander Gruber

@JasperLoy i found some embarassingly bad ones of my own about a year ago, haha

Peter Tamaroff

@AlexanderGruber Man, I was looking at some of my old questions.

user19161

@AlexanderGruber Exactly, after one hangs around here for a while, one realises that he wants to rewrite things in a better way.

Peter Tamaroff

I said $\lim\limits_{n\to\infty}$ was an abuse of notation because $\infty \notin \Bbb N$.

I insist on the use of $\lim$ alone.

user19161

12:53 AM

Again, note that one can edit at most 5 old posts a day, so with that limit, one should not be afraid of bumping.

Peter Tamaroff

I don't like $n\to\infty$.

Alexander Gruber

@PeterTamaroff i like that.

@PeterTamaroff lim all the way

Peter Tamaroff

@AlexanderGruber You like that I don't like it, or like what I don't like?

:confus:

Alexander Gruber

@PeterTamaroff i like $\lim$ instead of $\lim_{n\to\infty}$

Peter Tamaroff

@AlexanderGruber Right.

@AlexanderGruber Well, I can accept $\lim\limits_{n\to\infty}$, but $\lim_{n\to\infty}$ is bonfire worthy.

Alexander Gruber

12:57 AM

@PeterTamaroff how about stuff like $\frac{1}{n}\rightarrow 0$

Peter Tamaroff

@AlexanderGruber Hmmm, yeah, it's OK.

@AlexanderGruber Do you have any idea on the subgroup I talked in ${\rm SL}(2,\Bbb Z)$?

About half an our ago.

user19161

Why is the -1 times -1 post still being upvoted? Nobody is bumping it!

Peter Tamaroff

@AlexYoucis You?

Alexander Gruber

@PeterTamaroff i'm not sure: what's the question?

Peter Tamaroff

We have three @Alex in here!

Alexander Gruber

1:03 AM

@JasperLoy google it. maybe it got linked from somewhere.

Peter Tamaroff

@JasperLoy Which one?

user19161

@PeterTamaroff The one that got me the gold badge!

Peter Tamaroff

@AlexanderGruber To determine $\langle \alpha,\beta\rangle$.

Alexander Gruber

@PeterTamaroff ah, hm let me think about it

user19161

"we are offline"

Peter Tamaroff

1:04 AM

"Stack Exchange is currently offline, we'll be back shortly!"

Buuu!!!

user19161

BOO!!!

Peter Tamaroff

@AlexanderGruber See above the above.

user19161

Luckily we are already logged into chat!

Peter Tamaroff

$\alpha^2\beta=\beta\alpha^2$

$\alpha^4=1$

$\beta^3=1$

$|\alpha\beta|=\infty$

Alexander Gruber

@PeterTamaroff what do you want to know about $\langle \alpha, \beta \rangle$?

Peter Tamaroff

1:08 AM

@AlexanderGruber What it is.

I want to determine that subgroup.

Entirely.

Describe it, write it down, whatever you like to call it.

=)

Alexander Gruber

@PeterTamaroff right: so you want a presentation, or a formula for the elements, something liek that.

Peter Tamaroff

@AlexanderGruber Right.

Like I did here

Except this time it is infinite.

user19161

@AlexanderGruber And I wonder WHERE.

user19161

Maybe it came out in the monthly newsletter or sth, haha.

user19161

1

Q: Question on Q&A's

My friend gave a fun problem to me that went as follows: A. For how many of these questions is zero the answer? B. For how many of these questions is one the answer? C. For how many of these questions is two the answer? D. For how many of these questions is three the answer? ...

recreational-mathematics

user19161

1:20 AM

Guys, this question is BOSS!!!

user19161

@PeterTamaroff Goodnight Pedro, I am going to bed.

Peter Tamaroff

@JasperLoy Byes.

Alexander Gruber

1:39 AM

interseting how $b^a=-b$

Peter Tamaroff

@AlexanderGruber Ah?

Alex Youcis

@AlexanderGruber Tell me interesting group theory things

Peter Tamaroff

@AlexYoucis HAHAHAHAHA

amWhy

@AlexanderGruber interseting: interesting word ;-)

Alexander Gruber

@PeterTamaroff oh i meant $\beta^\alpha=-\beta$ with your matrices

@amWhy i ain't never purported to be able to spell, darlin'. :)

amWhy

1:49 AM

@AlexanderGruber hehehehe...

Peter Tamaroff

@AlexanderGruber That is $\alpha\beta \alpha^{-1}=-\beta$ yes?

Alexander Gruber

@AlexYoucis so if i've got a normal subgroup $X$ of $G$ such that $G/X$ has all sylow subgroups cyclic or generalized quaternion, i believe that $\ell_F(G)$ is bounded by $4$.

Alex Youcis

@AlexanderGruber What is $\ell_F(G$?

Alexander Gruber

@PeterTamaroff i think it doesn't matter - should be both

@AlexYoucis the fitting length of $G$.

Alex Youcis

@AlexanderGruber Hmm, interesting. I don't see the connection between cyclic and generalized quaternion. What property do they share that allows you to (hopefully) deduce this?

Alexander Gruber

1:51 AM

@AlexYoucis unique elements of order $p$.

Alex Youcis

@AlexanderGruber Ah, hmm. Interesting indeed.

@AlexanderGruber Tell me another! Or let me ask you a question :)

Alexander Gruber

@AlexYoucis yes indeed :)

@AlexYoucis did you decide on a school yet?

Alex Youcis

@AlexanderGruber Not officially, but probably Berkeley. You?

Alexander Gruber

@AlexYoucis good choice. me, probably florida.

Alex Youcis

@AlexanderGruber University of Florida?

Alexander Gruber

1:54 AM

@AlexYoucis yeah, at gainesville

@AlexYoucis it's where john thompson's at among other things

Alex Youcis

@AlexanderGruber Yeah, I knew Thompson was there. Is he still taking students?

Alexander Gruber

@AlexYoucis i don't think he can advise, but he's still cranking out papers.

Alex Youcis

@AlexanderGruber Ah, cool cool. So I assume that you are pretty hard-set on doing finite group theory?

Alexander Gruber

@AlexYoucis somewhat. i'd like to study it more in grad school anyhow. but who knows, i may find something else i like more.

Peter Tamaroff

Alex Youcis

1:58 AM

@AlexanderGruber That's fair enough dude. I wish I knew more finite group theory!

Alexander Gruber

@AlexYoucis so you'll be going to school with qiaochu then. did you meet him when visiting?

Alex Youcis

@AlexanderGruber I did not. I mostly hung out with my berkeley friends. We're not really interested in similar things anyway

Alexander Gruber

@AlexYoucis how do you have berkeley friends already? did you REU there?

Alex Youcis

@AlexanderGruber No, but I did an REU where a lot of Berkeley students attended

Alexander Gruber

ahhh, cool

Alex Youcis

2:01 AM

Tell me where I can learn more interesting group theory

:)

Alexander Gruber

you should buy isaacs book :)

it's definitely what taught me most

Alex Youcis

I've looked at it a lot!

Do you mean group theory, or character theory?

Alexander Gruber

i meant his finite group theory book

his character theory book is great too, but i do have another i prefer

Alex Youcis

Yeah, I need to read those both more

what are you interested in again--besides finite group tehroy?

Alexander Gruber

@AlexYoucis graph theory, cryptography

Alex Youcis

2:05 AM

Ah, interesting! Cool stuff!

Alexander Gruber

im trying to get into ring theory lately too but i don't know too much about it yet

(noncommutative i mean)

Alex Youcis

Graph theory is something I also knew I wish more about

That's something I've actually read a bit about

both of TY Lam's books

Alexander Gruber

i just started on lam's

Alex Youcis

both Lam and Bergman are at Berkeley

Alexander Gruber

i'm diggin his writing

Alex Youcis

2:07 AM

which is interesting

Alexander Gruber

wow, yeah. i'm definitely jealous. berkeley wouldn't even have looked at my app twice i'm sure.

Peter Tamaroff

@alex Though I don't know much about it, I'm interedted in whatever connection there is between Special Functions and Lie Theory.

Alex Youcis

@PeterTamaroff There is definitely connections! For sure. It isn't the most common interaction though

Alexander Gruber

@PeterTamaroff that is cool. i think lie theory is awesome too, i want to study it more. we don't have any classes at my uni on lie theory atm

Alex Youcis

@AlexanderGruber Don't be too jealous. You have Thompson!

Peter Tamaroff

2:08 AM

@AlexYoucis Have you heard of Truesdell's Essay?

Alex Youcis

@PeterTamaroff I have not.

Alexander Gruber

@AlexYoucis this is true :)

also warm weather, i'll tell you that made a huge difference in my decision

(not that berkeley doesn't of course)

i feel like lack of winter is going to double my productivity

Alex Youcis

@AlexanderGruber I feel like it will halve mine!

Alexander Gruber

@AlexYoucis oh yeah? winter person?

Alex Youcis

Definitely. Snow is so...mathy.

Alexander Gruber

2:11 AM

@AlexYoucis i suppose there is a certain sense in which constant sun and beaches will lower my work output.

Alex Youcis

Haha, yeah man. Florida should be awesome!

@AlexanderGruber Any interest in geometry?

Alexander Gruber

@AlexYoucis i really don't know enough yet to say. algebraic geometry is a big thing though, it's on my list of things to look into.

and a lot of people with similar interests to mine seem to enjoy it

Alex Youcis

Haha, that's respectable

sure, sure

Alexander Gruber

so what are your primary interests at this point?

Peter Tamaroff

@AlexYoucis It is called "An Essay Towards a Unified Theory of Special Functions."

Alex Youcis

2:15 AM

@AlexanderGruber I'm interested in a bunch of things. I'm doing like seven mathematical things this term haha

@PeterTamaroff Link me?

Peter Tamaroff

It is based a the functional equation $$\frac{\partial}{\partial z}
F(z,\alpha)=F(z,\alpha+1)$$

Alex Youcis

Where $F$ is...

Peter Tamaroff

@AlexYoucis Well, many different functions!

@AlexYoucis I can give you the full thing.

Alex Youcis

sure, send it on over

Alexander Gruber

@AlexYoucis are you purely algebra at this point? i seen some complex analysis on your blog sometime ago

Peter Tamaroff

2:18 AM

@AlexYoucis Here

Alex Youcis

@AlexanderGruber I'm pretty off of pure algebra. Number theory, algebraic geometry, complex geometry, algebraic groups, etc. are more my current interests

@PeterTamaroff ohgodtypewriterfont

Peter Tamaroff

@AlexYoucis It is awesome!

Awesome typewriter font!

I bow to the guys who wrote with that before.

Alex Youcis

@PeterTamaroff ohgodwy

Peter Tamaroff

@AlexYoucis HAHAHA

@AlexYoucis I want to read that some day.

And understand it.

And work on it.

Alex Youcis

@PeterTamaroff I can respect that, but I would rather not.

Peter Tamaroff

2:22 AM

After paying some poor soul to TeX it up.

@AlexYoucis Do you think it is too old, expired in some sense?

Alex Youcis

@PeterTamaroff I don't really know what it is, and I am nowhere even close to knowledgable about a field (I used to be into special functions and read parts of the book by Askey) so I can't say

Peter Tamaroff

@AlexYoucis Aha. What did you do again?

Alex Youcis

hmm?

Peter Tamaroff

@AlexYoucis I mean, what is your research area?

IIRC, you're "mathematically" older than I am.

Alex Youcis

I don't know yet. Probably something approximating arithmetic geometry

Peter Tamaroff

2:28 AM

@AlexYoucis What is that?

Alex Youcis

@PeterTamaroff Algebraic geometry minded towards arithmetic (number theory) problems

Peter Tamaroff

Like the guy who proved FLT? Wiles?

Alex Youcis

Yeah, that had an arithmetic geometry flair to it

not that I understand his paper haha

Peter Tamaroff

@AlexYoucis Hahhaha, right.,

Alexander Gruber

hey here's something i was wondering about earlier today

what area of math is fractal geometry a part of?

is it its own thing?

κρανίοπεριπολία

2:32 AM

I miss caveman :-(

Ethan

does anyone here know about L functions?

Alex Youcis

@AlexanderGruber I believe so. I don't know how many people actually study it. The very few I have encountered were very, very analytic. Fractal people are very proud of some fact in fractal geometry which is equivalent to the GRH

Alexander Gruber

@AlexYoucis that explains why i've never seen it.

Alex Youcis

@AlexanderGruber Yeaaaaaaaah

Ethan

Is there a proof of the non vanishing of $L(1,\chi)$ that doesn't use complex analysis?

Alex Youcis

2:34 AM

@Ethan Kind of. There is one that minmizes the use of complex analysis, but it has a fairly advanced flavor

κρανίοπεριπολία

Hi @Argon wazzup?

Argon

@κρανίοπεριπολία Not much! And how are you?

Ethan

@AlexYoucis how 'advanced' could you give me an idea of what tools are used?

κρανίοπεριπολία

@Argon Fine thanks.

Yo @JasperLoy

user19161

@κρανίοπεριπολία Hey hey.

Argon

2:36 AM

@JasperLoy Hey hey hey

user19161

@Argon Fun fun fun fun.

κρανίοπεριπολία

Friday song?

user19161

Indeed.

Argon

@JasperLoy Almost (sorta) Friday here too!

Alex Youcis

@Ethan It involves a bit of algebraic number theory--see here mathoverflow.net/questions/25794/…

user19161

2:37 AM

@Argon Is it a big occasion for you?

Argon

@JasperLoy Well, it is Rebecca Black day.

user19161

@Argon I mean for the Jewish people.

Argon

It happens around 52 times per annum

@JasperLoy Not particularly. It is part of an 8-day (7-day in Israel) holiday though, that began Monday night.

κρανίοπεριπολία

Good Friday!

user19161

@Argon Ah, then it is HUGE, lol.

Argon

2:39 AM

:)

κρανίοπεριπολία

TGIF is TGIGF

user19161

Perhaps a miracle will happen in my life this Good Friday...

Argon

@κρανίοπεριπολία Hahahahahah :)

κρανίοπεριπολία

:)

anon

I refuse to use ${\Bbb Z}_n$ for the cyclic group of order $n$, especially if $n$ is prime.

user19161

2:41 AM

@anon So what do you use?

Alexander Gruber

@anon do you $C_n$?

Ethan

whats $Z_n$

Peter Tamaroff

@Ethan ${\bf Z}_n$ is the cyclic group of order $n$.

Don't you know about groups? You're talking about Dirichlet characters and stuff...

Ethan

I don't know about groups

user19161

A group of people is any set of two or more people, lol.

Peter Tamaroff

2:49 AM

@anon What do you think of my answer?

@Ethan Then how did you get to characters?

user19161

@PeterTamaroff They were cartoon characters, lol.

Peter Tamaroff

@JasperLoy Totally unfunny!

user19161

@PeterTamaroff Yes, that is why it is so funny.

Peter Tamaroff

@JasperLoy I got no upvotes yet =/

user19161

@PeterTamaroff I have some coins to spare the beggar...

Peter Tamaroff

3:02 AM

@JasperLoy Well, I think it is worthy of coin.

Alexander Gruber

i did not think this guy was gonna stick around

user19161

@PeterTamaroff Anyway, I changed my mind. I think I will retire from MSE, lol.

Alexander Gruber

@JasperLoy the pension's not very good man

Peter Tamaroff

@JasperLoy Yeah, right.

"The kid who cried "wolf!"."

@AlexanderGruber What do you think of my answer, Alex?

anon

@AlexanderGruber yes

@PeterTamaroff linked to the wrong one, but fine

user19161

3:07 AM

@PeterTamaroff Hehe, still begging for coins!

Peter Tamaroff

@anon Yeah, I just noticed.

@AlexanderGruber LAWL. The guy said $\Bbb Z_9^\times$ was't a group. I'm curious about what he was thinking.

caveman

I've never seen this question math.stackexchange.com/questions/176760/… no I didn't downvote your answers

@JasperLoy, you are extremely rude and cruel

Peter Tamaroff

@caveman Hey, you're back!

Alexander Gruber

@PeterTamaroff it appears correct. :)

Peter Tamaroff

@Ethan

If you want a proof of the non vanishing of $L(1,\chi)$, you can consult Apostol's "Introduction to Analytic Number Theory", Chapter 6.

Ethan

3:15 AM

@PeterTamaroff I don't have the book

Peter Tamaroff

@Ethan Give me a sec...

Alexander Gruber

@PeterTamaroff he once got into an argument with me over whether a question was stupid or not (which was "what graph is the petersen graph isomorphic to")

Ethan

itself

Alexander Gruber

and ended it with "Alex you should go to bed you looks like sleepy"

Peter Tamaroff

@Ethan Here

I'd recommend you go through all the Chapter

Ethan

3:16 AM

@PeterTamaroff can you get me more books?

anon

down the rabbit hole

Peter Tamaroff

It starts out from scratch defining what a group is, and works nicely.

@Ethan Hey! Finish that one up first!

Ethan

its not loading ffs

Peter Tamaroff

@Ethan Sure?

Ethan

nvm I think its working now

Peter Tamaroff

3:19 AM

@Ethan I do recommend also that you look at previous chapters, since he uses some analytic derivations (some integral formulas and asymptotic) stuff from them too.

@anon What is your notation for the matrix ring of a ring $R$?

anon

For a matrix ring I use $M_n(R)$.

You want to be pretty careful with how you define it if $R$ is noncommutative.

Peter Tamaroff

@anon What needs care?

$(M\cdot M)_{ij}=\sum_{k=1}^n M_{ik}N_{kj}$, yes?

anon

Fun fact: for polynomials over a noncommutative ring, f(x)=g(x)h(x) as polynomials does not mean f(a)=g(a)h(a) for a given a in R (i.e. evaluation is no longer a ring homomorphism R[x]->R)

Peter Tamaroff

@anon LOL.

anon

$(M\cdot N)_{ij}$, yes. you can't interchange the M, N terms around.

Alex Youcis

3:34 AM

Do you know what I have used, so much, over the last year and half of my mathing, something that seems so pivotal to every area of mathematics (that I am interested in?)

Ooops, haha, sorry guys, I thought this was Gchat

apologies

anon

"Babe caught me sleepin"...

Alex Youcis

hahahahaha

yeah, you think so?

anon

heh heh

Alex Youcis

I can be passive agressive, but tha'd be a whole new level

haha

that was a very appropriate reference though

Peter Tamaroff

@anon What is the problem?

amWhy

3:51 AM

@Argon Hello! Haven't seen you for awhile!

κρανίοπεριπολία

Hi @amWhy nice to see you.

amWhy

@κρανίοπεριπολία Hello! Back to the keyboard!

κρανίοπεριπολία

...in motion.

amWhy

4:08 AM

@κρανίοπεριπολία Yes, indeed!

κρανίοπεριπολία

4:25 AM

@amWhy I get the impression of a central moment of clearly seeing the question.

Peter Tamaroff

4:37 AM

@anon

Let $R$ be commutative. Then $AB=1$ implies $BA=1$ in $M_n(R)$.

Peter Tamaroff

4:50 AM

@anon I'm trying to see who to work that up above.

I have that $$\sum_{k=1}^n a_{ik}b_{kj}=\delta_{ij}$$ and want to show $$\sum_{k=1}^n a_{ki}b_{jk}=\delta_{ij}$$

Peter Tamaroff

5:03 AM

@AlexanderGruber

I have a silly question

Alexander Gruber

yes

Peter Tamaroff

Why cannot we define determinants in non commutative rings?

Where $$\det A=\sum_{\sigma\in S_n}{\rm sgn}\sigma \prod_{k=1}^n a_{k,\sigma(k)}$$

Alexander Gruber

i don't see why you couldn't

it may just be that it isn't as useful as it is in the commutative setting

Peter Tamaroff

Maybe.

"It is easy to convince ourselves that the main formulas on determinants, which can be found in any text on linear algebra, are valid for determinants of matrices over any commutative ring. Thus if $R$ is commutative we can define for $A = (a_{ij})$ the ..."

Alexander Gruber

actually for example, i have used determinants in group rings.

i think that just says that so long as a ring is commutative, the determinant info will work as well as it did in $\mathbb{R}$ or $\mathbb{C}$ in linear algebra class

Peter Tamaroff

5:07 AM

@AlexanderGruber Did you see what I asked above?

@AlexanderGruber Yep.

30 mins ago, by Peter Tamaroff

Let $R$ be commutative. Then $AB=1$ implies $BA=1$ in $M_n(R)$.

Alexander Gruber

hm

good question

Peter Tamaroff

@AlexanderGruber Maybe I should ask on main?

I wanna try myself though.

However, I doesn't seem that easy.

I have an idea.

Suppose $AB=1$. This means $BABA=BA$, so $BA(BA-1)=0$, or $A(BA-1)=0$.

(upon left $A$ multiplication)

@AlexanderGruber Since $R$ is commutative $\det(AB)=\det A\det B=\det B\det A=\det(BA)=1$

JonnyQuiznos

5:34 AM

Hi there?

Where can I go to learn about the implicit function theorem?

Amzoti

@JonnyQuiznos: www.youtube.com/watch?v=xtgTckGMuWE,

Eugene

5:54 AM

@PeterTamaroff You clearly know that doesn't imply that BA is the identity though right?

Peter Tamaroff

@Eugene Gods, yes.

@Eugene Think you can help?

Eugene

let me think on it

oh

do this straight

might work

i dunno though

did you try that?

JonnyQuiznos

Does anyone know of the implicit function theorem?

I have a quick question

Peter Tamaroff

@Eugene Ah?

@Eugene Do what?

JonnyQuiznos

I have a function x^3+3xy^2+2y^3 = 1. and I need to find where it may not be possible to solve for y as a smooth function of x in
some neighborhood of the point?

Transcript for

$Mathematics$ Mathematics