Mathematics - 2019-06-10 (page 1 of 2)

Ted Shifrin

00:52

@StanShunpike It certainly doesn't. I'm guessing you're looking at one of the explicit definitions in terms of skew-symmetrizing tensor products. Different books are at odds about this. My definition has no denominator. I want the volume of the unit cube to be $1$, not $1/k!$. In the case of two vectors, I take $v\wedge w = v\otimes w - w\otimes v$, no factor of $1/2$.

Daminark

Hey Ted!

And Rithaniel!

Ted Shifrin

01:08

hi Demonark

You've morphed into a tortoise?

Daminark

01:23

This has been my profile picture for some time now

Turtle sloth

Or maybe a tortoise sloth

I googled "Turtle sloth" and this came up, can't distinguish them visually so I guess I'm trusting Google

Daminark

01:39

Hey @Karl!

Karl Kronenfeld

Sup @Daminark

northerner

05:40

Hi

ÍgjøgnumMeg

07:33

Morning all

Alessandro Codenotti

07:43

Morning

ÍgjøgnumMeg

How's it going? @Alessandro

Alessandro Codenotti

07:57

Quite well thanks

What about you?

Subhasis Biswas

alle

@AlessandroCodenotti

is $\phi(x)=\frac{3}{2}x$ going to be a homomorphism from $Z$ to $Q$ that is not an inclusion mapping

?

Alessandro Codenotti

Group hom?

Subhasis Biswas

yes

Alessandro Codenotti

Yes

Subhasis Biswas

ahaaa

ÍgjøgnumMeg

08:04

@Alessandro I'm alright, just at work reading Weibel

lol

and chewing on Rennie for heartburn

ouch

Subhasis Biswas

@AlessandroCodenotti , can you give me an exercise?

Alessandro Codenotti

@ÍgjøgnumMeg Weibel?

@SubhasisBiswas In which subject?

Subhasis Biswas

either linear transformations (regarding rank-nullity) or group theory

Alessandro Codenotti

Here's a tricky one. Suppose that $H$ and $G$ are two groups such that $H$ is isomorphic to a subgroup of $G$ and $G$ is isomorphic to a subgroup of $H$. Must $H$ and $G$ be isomorphic?

ÍgjøgnumMeg

@Alessandro homological algebra

Alessandro Codenotti

08:13

(In other words does the category of groups have the Schröder–Bernstein property?)

@ÍgjøgnumMeg Ah I see, not really my cup of tea

I'm reading the Homotopy Type Theory book at the moment

ÍgjøgnumMeg

@Alessandro I think it's necessary for anything I want to do

nice :)

Alessandro Codenotti

@ÍgjøgnumMeg Well it's used a lot

ÍgjøgnumMeg

Right

Subhasis Biswas

@AlessandroCodenotti wow

Alessandro Codenotti

(I've seen very little homological algebra, the bare minimum needed to set up the $\mathrm{Tor}$ and $\mathrm{Ext}$ functors)

ÍgjøgnumMeg

08:15

Tor and Ext measure the exactness of hom and tensor right?

Alessandro Codenotti

The other way around

ÍgjøgnumMeg

Ext measures exactness of hom and Tor of tensor?

errr

other way around

hahaha

Alessandro Codenotti

The way I remember it is that Tor is related to torsion and tensoring with $\Bbb Q$ kills it

ÍgjøgnumMeg

orly

group homology can be defined in terms of tor

nice

Alessandro Codenotti

Uh I have no idea about group (co)homology

ÍgjøgnumMeg

08:22

me neither

lol

Alessandro Codenotti

Mathei is the right person to ask

Leaky Nun

08:51

the way I remember it is tor -> [t]ens[or]

mick

09:05

Hi all

0

Q: Diophantine $\frac{a^2 + b^2}{ab + 1} = \frac{c^2}{d^2} $

Consider the Diophantine equation with $a,b,c,d > 0$ : $$\frac{a^2 + b^2}{ab + 1} = \frac{c^2}{d^2} $$ For the case $d=1$ , this is a Classic ; we know that Diophantine $\frac{a^2 + b^2}{ab + 1} = K $ implies $K$ is a square. This is the standard example of the so-called vièta jumping. Altho...

ÍgjøgnumMeg

@Leaky tf man

Leaky Nun

what

my brain made those associations

can't help

ÍgjøgnumMeg

hahaha fair

Ho[ex]m[t]

s.harp

09:51

@ÍgjøgnumMeg whats hoexmt

ÍgjøgnumMeg

10:07

was just a joke lol

mick

0

Q: $\frac{f_3(a,b)}{g_3(a,b)} $ always a cube?

Let $a,b,c,n$ be positive integers and let $f_n(a,b),g_n(a,b) $ be integer polynomials with variables $a,b$. Now consider the diophantine equation : $$ \frac{ f_n(a,b)}{g_n(a,b)} = c^n $$ We know that if and only if $g_2(a,b)$ divides $f_2(a,b)$ $$ \frac{ f_2(a,b)}{g_2(a,b)} = c^2 $$ Is al...

number-theory diophantine-equations cubic-equations vieta-jumping

MatheinBoulomenos

@ÍgjøgnumMeg any questions about group cohomology?

ÍgjøgnumMeg

@Mathein no not really, I'm just looking into homological algebra atm aiming towards group cohomology for number theory

:)

MatheinBoulomenos

yeah group cohomology is really useful for NT

ÍgjøgnumMeg

class field theory can be done entirely through group cohomology right?

MatheinBoulomenos

10:11

right

that's how we did it in our courses

ÍgjøgnumMeg

Sounds like fun

MatheinBoulomenos

it was a bit technical at times, but yes, it was quite fun

ÍgjøgnumMeg

the "coefficients" part of cohomology modules are representations right?

MatheinBoulomenos

yeah basically. Representations are $k[G]$-modules, for group cohomology you're looking at $\Bbb Z[G]$-modules

but representations do play a role. If $M$ is a $\Bbb Z[G]$-module, then $M/pM$ is a $\Bbb F_p[G]$-module, i.e. a representation

ÍgjøgnumMeg

Nice :)

well I better get a handle on it between now and october

Leaky Nun

10:19

@MatheinBoulomenos I'm proving 01I1 in Lean now

it's more tedious than it looks

MatheinBoulomenos

well, it does look tedious

Leaky Nun

but I'm also learning in the process

@MatheinBoulomenos e.g. I learnt that for any locally ringed space you can define $D(f)$

ÍgjøgnumMeg

10:38

1 month of rainfall is due to fall in 6 hours today

in Plymouth

lol

@Mathein Komische Frage: mit welcher Bank hast du ein Konto?

hahaha

Mathphile

11:22

is $\lfloor \zeta(-n) \rfloor$ only prime for $n=23$ ?

mick

0

Q: $\frac{f_3(a,b)}{g_3(a,b)} $ always a cube?

Let $a,b,c,n$ be positive integers and let $f_n(a,b),g_n(a,b) $ be integer polynomials with variables $a,b$. Now consider the diophantine equation : $$ \frac{ f_n(a,b)}{g_n(a,b)} = c^n $$ We know that if and only if $g_2(a,b)$ divides $f_2(a,b)$ $$ \frac{ f_2(a,b)}{g_2(a,b)} = c^2 $$ Is al...

number-theory diophantine-equations cubic-equations vieta-jumping

Larry Eppes

11:53

Hello.

Could anybody explain to me, how to get 5.5, 5.6 from 5.4 in this page farside.ph.utexas.edu/teaching/336L/Fluidhtml/node68.html ??

is that $ds=\partial(-y,x)$ in vector form

Mathphile

12:33

0

Q: Is $\lfloor \zeta(-n) \rfloor$ only prime for $n=23$?

I searched for primes of the form of $\lfloor \zeta(-n) \rfloor$, where $n \in \Bbb{N}$, for a range of $n \le 10^4$ on PARI/GP and found $\lfloor \zeta(-n) \rfloor$ is only prime for $n=23$. My PARI code: for(n=1, 10^4, if(ispseudoprime(floor(-bernfrac(2*n)/(2*n)))==1, print([2*n-1, floor(-be...

number-theory prime-numbers riemann-zeta conjectures

Martin Sleziak

13:12

Image is broken — Akiva Weinberger Oct 29 '18 at 11:59

@AkivaWeinberger I will just mention that the image in the post with the above comment has been restored: Can knot diagrams be monotonically simplified using under moves? mathoverflow.net/posts/186178/revisions

I commented here rather than on MO - since I did not want to leave many redundant comments there.

Akiva Weinberger

13:44

Ah cool, thanks @MartinSleziak

Subhasis Biswas

14:05

@AlessandroCodenotti

Alessandro Codenotti

?

Subhasis Biswas

The result doesn't hold, right?

been thinking about it for quite a while

Alessandro Codenotti

Do you have a counterexample?

Subhasis Biswas

@AlessandroCodenotti I have an idea for a counterexample...which I need a little help with

$Z \times Z \times Z ...$ and $Z \times Z \times Z ... Z_2$

Martin Sleziak

Well, the thanks for recovering the dead image goes mainly to Glorfindel who created the script/bot for such purposes.

Subhasis Biswas

14:07

infinite product .

my main idea is to take two groups, such that they are generated (if that is the terminology) by infinite number of elements, yet they differ slightly

I need some help regarding this. or at least some indication whether or not I am heading in the right direction.

Alessandro Codenotti

@SubhasisBiswas this is close to a working example, however now subgroup of the first is isomorphic to the second

Subhasis Biswas

@AlessandroCodenotti right direction?

Alessandro Codenotti

definitely

Subhasis Biswas

how do I do the other direction?

a little hint

$f: Z \times Z \times Z... \to Z \times ... Z_2$ with $f(a_1,a_2,...)=(a_1,a_2,...,\overline{0})$

Alessandro Codenotti

Sure, the problem you have now is that there is no injection in the other direction

Subhasis Biswas

14:19

@AlessandroCodenotti okay, I have to remove this obstacle

so, what if I adjoin more parts...

like

Alessandro Codenotti

Because there are no elements of order $2$ in $Z\times Z\times\cdots$ so you don't know where to send $(0,0,0,\ldots,\overline{1})$

Subhasis Biswas

$Z \times ... Z_2 \times Z \times....$

Alessandro Codenotti

That's not going to help, you have an element of order $2$ on one side and no element of order $2$ in the other

Subhasis Biswas

@AlessandroCodenotti yes

@AlessandroCodenotti okay. I will think some more

will let you know

Alessandro Codenotti

Hint: let $G=Z\times Z\times Z\times\cdots$. You want to add to $G$ an element of order $2$ to make an injection $G\times Z_2\to G$ possible. Of course the easiest way is to look at $G\times Z_2$, but that would not be a counterexample anymore. Next up is $G\times Z_4$, now you have an injection $G\times Z_2\to G\times Z_4$, but the backward direction is problematic

So to make the backward direction possible you could look at $G\times Z_4\times Z_2$ and $G\times Z_4$, now the direction $G\times Z_4\to G\times Z_4\times Z_2$ works and the other one is problematic...

Akiva Weinberger

14:32

Oh, that leads to a different solution than the one I was thinking of

Alessandro Codenotti

@AkivaWeinberger DC, I don't want to spoil it here

Subhasis Biswas

yeah, don't do it

Secret

Solving linear diophataine equations is common in linear programming problems when one only want integer solutions:

wolframalpha.com/input/…

user131753

Which problem are you people talking about @AlessandroCodenotti?

Alessandro Codenotti

If $G$ and $H$ are two groups such that $G$ is isomorphic to a subgroup of $H$ and $H$ is isomorphic to a subgroup of $G$, must $H$ and $G$ be isomorphic?

Elsa

14:44

Could anyone please explain what is the definition of the following expression; $\lim_{|z| \to \infty}f(z)$ ? . As I recall we haven't defined it strictly on my complex analysis class, yet the intuition behind it is pretty clear.

Akiva Weinberger

> When someone has come to you for your expertise and your expertise has failed, what do you have left? You have only your character to fall back upon–and sometimes it’s only your pride that comes through.

- Atul Gawande, Better: A Surgeon's Notes on Performance

Elsa

Actually , the intuition is not clear for me at all. I seriously don't understand anything about that limit.

Akiva Weinberger

Informally: if, for any complex number $z$ far away from the origin, $f(z)$ is near the same number $L$, then the limit is $L$

As an example, take $f(z)=1/z$

user131753

@Elsa Think of for the time $f$ to be a real valued function of a real variable. How would you define formally (i.e., using $\varepsilon-\delta$) $$\displaystyle\lim_{x\to\infty} f(x)=L$$ (assuming of course the limit exists)?

Akiva Weinberger

If $z=-1000$, or $z=1000i$, or $z=1000$, we still have $f(z)\approx0$

so $\lim_{|z|\to\infty}f(z)=0$

On the other hand, take $f(z)=e^z$

If $z=-1000$, $~f(z)\approx0$. If $z=1000$, $~f(z)\approx+\infty$.

If $z=2000\pi i$, $~f(z)=1$. If $z=2001\pi i$, $~f(z)=-1$.

So, $\lim_{|z|\to\infty}e^z$ does not exist.

Elsa

14:53

@user170039 I know the definition for the real valued functions. So you're saying it's analogous ?

Akiva Weinberger

Yeah

Elsa

Aha

user131753

@Elsa Yep. Just write it down and I will show the analogy.

Subhasis Biswas

$(Z \times Z \times Z...) \times (... \times Z_{16} \times Z_8 \times Z_4 \times Z_2) $ and $(Z \times Z \times ...) \times (...\times Z_{16} \times Z_8 \times Z_4)$ @AlessandroCodenotti

Elsa

Lemme try

Alessandro Codenotti

14:55

@SubhasisBiswas This works, and the $Z\times Z\times Z\cdots$ part is superfluous now!

Subhasis Biswas

@AlessandroCodenotti i guessed so

that part is redundant

ÍgjøgnumMeg

@Alessandro this is the solution I was thinking of after I looked at the property on wikipedia hahaha

Alessandro Codenotti

Another example is $G=Z_4\times Z_4\times Z_4\times\cdots$ and $H=G\times Z_2$

Subhasis Biswas

i had to build this from scratch

ÍgjøgnumMeg

Alessandro Codenotti

14:56

Yet another example (credits to @Akiva) is $G=F_3$ and $H=F_2$, where $F_n$ is the free group on $n$ generators

Subhasis Biswas

@AlessandroCodenotti the one you were hinting me at?

Alessandro Codenotti

yep

Subhasis Biswas

@AlessandroCodenotti wait. I have check what a free group is

@AlessandroCodenotti we got three examples wtf

Elsa

@user170039 im new to latex so this would take a lot of time for me. But I understand it now. Thanks, also thanks to @AkivaWeinberger

Akiva Weinberger

A free group on two generators (call them $a$ and $b$) is essentially the group of any words you can make out of $a$, $b$, $a^{-1}$, and $b^{-1}$

with the rule that you can get rid of $aa^{-1}$ etc

user131753

14:58

No problem @Elsa.

Subhasis Biswas

@AlessandroCodenotti worth it. Really.

Akiva Weinberger

so for example, $aba^{-1}b^3a$ is an element of this group

Subhasis Biswas

4 hours of thinking worth the while

anakhro

@user170039 I would agree that hate was a strong word.

Especially for someone who probably enjoys math in general.

Akiva Weinberger

Two elements of the free group are equal iff they're "obviously" equal (like $abb^{-1}a=a^2$ for example)

It's not obvious that $F_3$ is isomorphic to a subgroup of $F_2$

That could be another puzzle

Subhasis Biswas

15:00

@AkivaWeinberger what is "obviously"?

Akiva Weinberger

If you can turn one into the other by things that you can do in any group (such as get rid of $bb^{-1}$, or rewrite $aa$ as $a^2$)

Subhasis Biswas

@AkivaWeinberger hmmmmm....

Akiva Weinberger

Wikipedia explains it better than I do

Every vertex of this graph corresponds to an element of $F_2$

Subhasis Biswas

@AkivaWeinberger does that mean that we can take any sort of collection of them, like $a^2b^4a^2b^7...$ (paying attention to the order, like in permutation)

Akiva Weinberger

@SubhasisBiswas Yeah, that's an element of $F_2$

assuming it's finitely long

user193319

15:03

I am trying to prove that $Aut(D_8) \cong D_8$ using the fact that $D_8 \triangleleft D_{16}$. I also know that $|Aut(D_8)| \le 8$, but I'm not sure that that is helpful...I could use a hint,

Akiva Weinberger

The point is, there's no nontrivial relations between $a$ and $b$

Subhasis Biswas

@AkivaWeinberger $F_3$ is with $a,b,c , a^{-1}, b^{-1},c^{-1}$?

Akiva Weinberger

Yes

Again, it's not immediately obvious why $F_3$ is isomorphic to a subgroup of $F_2$

Subhasis Biswas

@AlessandroCodenotti, what deeper insights your exercise provides?

Alessandro Codenotti

The equivalent of the Schroeder-Bernstein theorem for groups is false

Akiva Weinberger

15:05

In fact, $F_\infty$ (the free group on $a_0,a_1,a_2,\dots$) is isomorphic to a subgroup of $F_2$

Alessandro Codenotti

(check DC again @Akiva)

Subhasis Biswas

@AlessandroCodenotti anything else?

Alessandro Codenotti

Not really I would say

Subhasis Biswas

@AkivaWeinberger didn't expect that. Will try to understand these. Wish I was smarter to grasp all these details so fast

Akiva Weinberger

Yeah it's surprising isn't it

Subhasis Biswas

15:06

@AkivaWeinberger does $F_2$ contain $F_3$?

Akiva Weinberger

It contains an isomorphic copy of $F_3$

Subhasis Biswas

@AlessandroCodenotti any suggestions for me? how am I doing (mathematically)? I need to know I stand where.

@AkivaWeinberger $F_2$ is the boss?

Akiva Weinberger

The best proof I know of this involves pictures

Subhasis Biswas

does $F_2$ contain the isomorphic copies of every other free groups?

Akiva Weinberger

Well, I already said $F_2$ contains $F_\infty$

and clearly $F_\infty$ contains all the others, doesn't it?

user193319

15:09

I believe only the countably generated free groups

Akiva Weinberger

And all the others contain $F_2$

So if what I said is true, then every $F_n$ ($n=0,1,2,\dots,\infty$) contains every other one

Subhasis Biswas

@AkivaWeinberger I didn't get this.

Akiva Weinberger

Every element of $F_2$ is an element of $F_3$, for example

I meant $F_2\subseteq F_3\subseteq F_4\subseteq\dotsb$

Subhasis Biswas

@AkivaWeinberger yes yes... just by putting $cc^{-1}$ at the end of each "string" generated by $a,b, a^{-1} , b^{-1}$.

Akiva Weinberger

($F_1$, for the record, is isomorphic to $\Bbb Z$)

($n\leftrightarrow a^n$)

Subhasis Biswas

15:14

@AkivaWeinberger yep. Clear.

Akiva Weinberger

($a^3$ is a "string" of those symbols because it's shorthand for $aaa$, similarly $a^{-3}$ is shorthand for $a^{-1}a^{-1}a^{-1}$)

(just to make sure that the definition I gave makes sense for those)

Did you learn about the abelianization of a group?

Note that the abelianization of $F_n=\Bbb Z^n$

Subhasis Biswas

@AkivaWeinberger not at all.

Akiva Weinberger

Oh

Never mind then

Subhasis Biswas

nope. I will learn about it.

okay. So, $F_2$ is contained in others. And $F_{\infty}$ is isomorphic to a subgroup of $F_2$. Yet the groups are not isomorphic?

Akiva Weinberger

Right

Subhasis Biswas

15:18

wow

user193319

If that surprises you, you should look at the free group isomorphism problem in the theory of von Neumann Algebras.

Huge open problem about whether the group von Neumann Algebras $LF_n$ and $LF_m$ can be isomorphism if $n \neq m$>

Akiva Weinberger

I don't think I know enough to know what a von Neumann algebra is

Subhasis Biswas

that's not for me though, right now. Anyway, I will try to remember what you said, although I don't understand it.

user193319

$LF_n$ is called the free group factor.

Akiva Weinberger

Do I need to learn functional analysis for that?

user193319

15:20

Yeah, some FA helps; but there is a lot of FA that you probably don't need.

Leaky Nun

@AlessandroCodenotti I just finished proving 01I1 in Lean

it took 1104 lines

user193319

Von Neumann algebra

In mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. It is a special type of C*-algebra. Von Neumann algebras were originally introduced by John von Neumann, motivated by his study of single operators, group representations, ergodic theory and quantum mechanics. His double commutant theorem shows that the analytic definition is equivalent to a purely algebraic definition as an algebra of symmetries. Two basic examples of von Neumann algebras are as follows: The...

Subhasis Biswas

@LeakyNun are you in undergrad?

Leaky Nun

yes

user193319

Operator Algebras is the coolest branch of mathematics.

Subhasis Biswas

15:22

@LeakyNun what is your course structure?

Leaky Nun

be more specific?

Subhasis Biswas

is it a 4 year course?

I am just curious how did you get to study Sheaves at so early stage?

Akiva Weinberger

I think I could never become a doctor

I dunno if I could deal with that emotionally

Subhasis Biswas

@AkivaWeinberger what did you become

Akiva Weinberger

I haven't finished school yet

Leaky Nun

15:26

@SubhasisBiswas interest

Akiva Weinberger

I don't think I could deal emotionally with patients dying, is what I mean

Subhasis Biswas

@AkivaWeinberger and how old are you

Akiva Weinberger

19

I start college in a few months

Subhasis Biswas

@LeakyNun damn. Keep it up.

Akiva Weinberger

I only say this 'cause I'm reading a book by a surgeon

and I keep on getting emotional

I almost never get emotional for basically anything

Rithaniel

15:30

I didn't know you were so young, Akiva

Subhasis Biswas

tbh I am also 19. But a lesser mortal compared to other guys here

Akiva Weinberger

lol

Subhasis Biswas

:p

Akiva Weinberger

no

but thanks

Subhasis Biswas

perhaps I am meant to be doing something other than math. I am a very undisciplined student.

Akiva Weinberger

15:32

@Rithaniel How've you been doing

Subhasis Biswas

i am afraid it is too late to be fixed.

Rithaniel

I've been doing well. Doing some administrative work at the college over the summer and thinking a lot about grad school.

Subhasis Biswas

@AkivaWeinberger it is better not to. Don't let other things interfere with your mathematics.

Rithaniel

Also, you're likely much more disciplined than me, subhasis. I dropped out of college the first time and tried doing other, more foolish, stuff.

Akiva Weinberger

By "emotional" I meant, like, crying, I didn't mean having emotions

I think having emotions takes precedence over math

Rithaniel

15:34

Must be a powerful book.

Subhasis Biswas

@Rithaniel well. I flunked my second semester. :p

thought about dropping out that very same day when my 2nd semester exams were going on.

my friends talked some sense to me. Calmed myself down.

Akiva Weinberger

Do you know what job you want to do?

and/or what you want to do with yourself in four years

Subhasis Biswas

@AkivaWeinberger that's a question I keep asking myself. Never got a sure answer.

Akiva Weinberger

'Cause, like, if the classes you're taking aren't towards that goal

then what's the point of stressing over their exams

Subhasis Biswas

@AkivaWeinberger it's a part of our syllabus. The paper was on Co-ordinate geometry (2d and 3d), which I hate with a passion

I will have to retake that paper again to finish my degree.

Akiva Weinberger

15:40

What's the degree in

Subhasis Biswas

BSc honours in Math

outdated course structure.

and very impractical (to my knowledge)

Akiva Weinberger

I met a lot of people this year who wanted to discourage me from going to college

You kind of have to have a good answer, at least to yourself, of why you want to do this

Subhasis Biswas

@AkivaWeinberger you are meant to be in the academic sphere.

that's your place. That's the place where you will grow.

Akiva Weinberger

And you know this how

Subhasis Biswas

@AkivaWeinberger very important actually.

@AkivaWeinberger your interest in mathematics

Rithaniel

15:45

Part of the issue with some degrees is how they're structured. I didn't really know if what I wanted was a degree in math until I took a proofs course, which, with the way things were structured where I am, didn't begin until my seventh semester.

Akiva Weinberger

(I spent the past year in Israel, so there were a lot of very religious people who were against the concept of colleges/universities and wanted everyone to study in a Yeshivah for the rest of their life)

(I leave in a week)

Subhasis Biswas

@AkivaWeinberger get out of that country

Akiva Weinberger

In a week, I said :P

Subhasis Biswas

you better do. Otherwise a life long regret will ensue.

Akiva Weinberger

I'm in Jerusalem right now

Rithaniel

15:47

I was flip-flopping between aerospace engineering and chemical engineering and math up until then.

Akiva Weinberger

My assumption right now is that I'll end up in academia, but I want to take engineering classes just in case

and probably also comp sci and finance

Rithaniel

(Hmmm, I am getting some lag. About seven messages popped up all at once)

Akiva Weinberger

I have until September(?) to figure this out

Subhasis Biswas

@Rithaniel what's your degree?

Rithaniel

Comp Sci will be a massive help in any kind of field you end up in.

I'm a BS in abstract math.

Akiva Weinberger

15:49

True

And I mentioned here before that I want to learn Japanese

And there's liberal arts classes that you're required to take

Subhasis Biswas

@Rithaniel aahhh.. tru

Akiva Weinberger

so I think I'll have to take something in literature

or history

Subhasis Biswas

@Rithaniel You want to do a phd?

Akiva Weinberger

neither of which are my strong suits

Rithaniel

I do plan on aiming for a Ph.D. but most plans for that put it about 6-7 years away.

Akiva Weinberger

15:51

I always found the acronym BS somewhat humorous

(sorry)

Rithaniel

In fact, most of my thoughts lately have been bent around how I would want to approach grad school for a Ph.D.

Oh yeah, I'm a bulls*** in abstact math.

Meanwhile a BA is Bad-A**

Akiva Weinberger

Fun fact: there's a cookbook called Good and Cheap that the author made available for free online, that's aimed for people living on $4 a day

Rithaniel

That sounds excellent.

Subhasis Biswas

see you guys

:)

will be back

was nice talking to you

Rithaniel

Cya Subhasis

Perturbative

16:25

Hey everyone!

So I'm preparing for the GRE

What's a good calculus book I should pick up to prepare? The standard one I'm used to is James Stewart's one, though I'm not sure if there are better alternatives

I guess Hubbard and Hubbard is a good alternative

ÍgjøgnumMeg

16:52

@Perturbative @Daminark took it!

(sorry to keep tagging @Daminark)

Perturbative

Thanks @ÍgjøgnumMeg I'll chat to Dami when he comes online

How's things going on your side? @ÍgjøgnumMeg

ÍgjøgnumMeg

@Perturbative not bad thanks :) I start my masters in october so I'm veeery excited

How about you?

Perturbative

Nice! If I'm not mistaken you were worried about your master's application a while back, really glad things worked out in the end! :) Things aren't going too bad on my side either, looking forward to my bachelor's thesis which I'm about to start, and to the GRE

Érico Melo Silva

@Perturbative any way to do a shit load of calc problems will help w the gre

ÍgjøgnumMeg

@Perturbative the main worry was about funding so I had to postpone for a while to work for a year, but I got a scholarship now! :D

@Perturbative nice, what are you gonna write about?

Akiva Weinberger

17:06

What's the 3D equivalent of a straightedge-and-compass construction? Instead of just lines and circles do you add planes, cones, cylinders, and spheres?

Leaky Nun

17:26

@AkivaWeinberger just take the quadratic closure of $\Bbb Q$

and take its cartesian cube

Akiva Weinberger

I know that'll be the set of constructible points

but what should the allowed operations be

Math geek

17:48

4

Q: $f$ be an analytic function defined on $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$

I came across the following problem that says: Let $f$ be an analytic function defined on $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$ such that the range of $f$ is contained in the set $\mathbb{C}\setminus (-\infty,0]$. Then $f$ is necessarily a constant function. there exists an analyt...

complex-analysis

please help me to give examples for option 3 and 4

if you provide example for 3. i can construct similar one for 4.

MatheinBoulomenos

@ÍgjøgnumMeg Sparkasse

Miksu

@AkivaWeinberger I read about the constructions in field theory one time when I was in high school so I don't really remember anything about them anymore, but shouldn't you just be able to construct the points on a plane exactly the same way as in 2d and then translate the points around with planes?

So you'd only need planes and maybe spheres in addition to lines and circles

Perturbative

18:13

@ÍgjøgnumMeg Sorry for the late reply, great to hear that you got a scholarship! :) With regards, to my thesis, my topic is spectral sequences in algebraic topology, hopefully, I'll compute the homotopy groups of some spheres and also prove some homotopy-theoretic theorems using spectral sequences

@ÉricoMeloSilva Aye, that I shall do. Quick question do you by any chance have the GRE prep materials from the UChicago 2018 REU? (assuming you went to the 2018 REU of course)

ÍgjøgnumMeg

18:29

@Perturbative nice :) Enjoy it, it was the best part of my undergrad by far lol

@Mathein okey cool :D

Érico Melo Silva

19:00

@Perturbative nah i never did the reu, amin did tho so ask him

Transcript for

$Mathematics$ Mathematics