Mathematics - 2016-06-26 (page 1 of 6)

Mike Miller

12:00 AM

$\Bbb Z/n$ for all $n$...

Ted Shifrin

I said non-planar, @MikeM.

From the picture, I can't tell. I doubt I see $A_5$ or $S_5$.

or the double-cover of $A_5$?

Mike Miller

I'm thinking of all the elliptic 3-manifolds. Many of them are quotients of $SO(3)$ by a finite subgroup.

Double cover lives in SU(2); it's the f.g. of the Poincare sphere. A_5 is the icosahedron group.

Ted Shifrin

@tern? :)

Semiclassical

what i'm thinking is to consider what permutations are allowed of $(x,y,z,-x,-y,-z)$

arctic tern

@TedShifrin all of the symmetries I described for the previous equation seem to apply to that one just as well

Ali Caglayan

12:03 AM

it doesn't look like a tetrahedron

Ted Shifrin

I agree, tern, but are we sure there aren't any others? I bet with you.

@Ali: There are various semi-regular polyhedra that don't look at all like the standard ones but have only those symmetry groups.

Let me find a picture to upload (from my algebra book).

Martin Sleziak

I'll repost this here - just in case somebody has a suggestion about that:

in Linear & Abstract algebra, 3 hours ago, by TheGreatDuck

@MartinSleziak is there a good place i can go to read on how tensors are multiplied?

Ted Shifrin

Here's a fun one, @Ali.

Ali Caglayan

Its hard to unsee the star

Ted Shifrin

Or this.

Ali Caglayan

12:09 AM

So what symmetries do they have?

Or do I find this out later

Do you go through them in your abstract algebra geometry book?

Ted Shifrin

You can figure it out for yourself. I'm telling you it has to be the symmetries of either a tetrahedron or (cube/octahedron) or (icosahedron/dodecahedron).

Mike Miller

What annoys me slightly is that not all finite subgroups of $SO(4)$ acting freely on $S^3$ are subgroups of $SU(2)$

Ted Shifrin

Well, why should everything be spin, @MikeM?

Mike Miller

Hm? $SO(4)$, not $SO(3)$

Ted Shifrin

Oh, right.

But why should a real action come from a complex action?

Mike Miller

12:12 AM

Would make my life easier.

Ted Shifrin

Oh, well, let's change all of math for you, then.

Mike Miller

Sure, that'd be great.

Ted Shifrin

And all smooth functions are holomorphic, too.

Mike Miller

There's a paper I like (depending on the day) whose results only work for $SU(2)/G$. Sad...

Don't be silly, I know the difference between random functions and those that satisfy an analytic elliptic PDE. :)

Ted Shifrin

Well, I wouldn't quite say smooth = random, but I take your point.

@Ali: Have you decided?

Mike Miller

12:15 AM

Nobody ever likes my answer of "why is complex analysis so nice?" with "Linear elliptic PDE have extremely nice solutions"

Ted Shifrin

I prefer the Cauchy kernel, myself. :P

Mike Miller

Same answer, though.

Ted Shifrin

Not entirely obviously, though.

That Bryant (Chern) paper @PVAL posted about $S^6$ has some cool stuff in it.

Ali Caglayan

@TedShifrin That first one seems to have icosahedron symmetry

I guess thats the easy bit

Mike Miller

You want to teach it to me?

Ted Shifrin

12:17 AM

Yup @Ali

What about the second one?

I certainly don't know it all, @MikeM.

I'm just a lot better at structure equations and the Cartan game than you are, @MikeM.

I've never worked with $G_2$, however.

Mike Miller

I don't know much about $G_2$. I know the tiniest iota about $G_2$ manifolds. :P

Obviously my perspective on them is different than Bryant's and Chern's.

Ted Shifrin

Well, I know nothing (to quote Sgt. Schultz).

Ali Caglayan

@TedShifrin The second one has tetrahedral?

Ted Shifrin

I don't think so, @Ali.

Mike Miller

Donaldson has an idea (program? maybe not quite so developed) on how to develop invariants of deformation classes of $G_2$ structures. There should be a Floer-type theory of manifolds and cobordism maps with CY 3-folds, $G_2$-manifolds and Spin(7)-manifolds.

Ted Shifrin

12:20 AM

NO elements of order $4$ in the tetrahedron group, @ali.

I still know nothing, @MikeM. Besides, I'm old and retired.

Mike Miller

So far there are some issues. One guy is making progress on defining a G_2 Casson invariant. You count instantons. Unfortunately a naive count might be 6 for one G_2 structure and 7 for another.

That's no good.

Ted Shifrin

Why? If you have different structures?

Mike Miller

Sorry, in the same deformation class.

Ted Shifrin

Oh.

Mike Miller

Bubbling-type problems. I don't know if that means anything to you.

Ted Shifrin

12:22 AM

Yes, I know about Sachs-Uhlenbeck bubbling.

Or I once did.

Mike Miller

It's my damn life.

Ted Shifrin

Lawson's CBMS lectures were fabulous. We did a year-long seminar on that.

I think I told you that before. Sadly, I threw all those notes away too.

Lots of cool, cool stuff in your math life, @MikeM.

Mike Miller

"Bubbling occurs starting in dimension 8. In this work we use only manifolds of dimension at most 6."

Yeah. If only I could write it down ...

Ted Shifrin

@Ali: If my picture isn't clear enough, google "truncated cube."

Ali Caglayan

that gave it away :P

Ted Shifrin

12:24 AM

nods

Ali Caglayan

I was trying to see if it was cut from something

Tetrahedron works if you ignore most of the shape

Ted Shifrin

It's way past your bedtime, anyhow :)

Ignoring most of the shape isn't cool for symmetry.

Ali Caglayan

but its a saaaatturrrddaayyy

Ted Shifrin

ohhhh

Ali Caglayan

or it was

Ted Shifrin

12:26 AM

yeah, it ain't no more ...

Ali Caglayan

ok then good night @TedShifrin

Ted Shifrin

Isn't it like 2:30 AM?

MathWanderer

Hello!

Ali Caglayan

1:30

Ted Shifrin

g'night, @Ali. Always a pleasure to chat with you.

Ali Caglayan

12:27 AM

Not that bad

Ted Shifrin

hi @MathWanderer.

MathWanderer

@TedShifrin Are you the professor who wrote

Ali Caglayan

Good night everybody else

MathWanderer

books in the linear algebra?

Ali Caglayan

Hope you all sleep as well as I am about to

Ted Shifrin

12:27 AM

A book, yes, @MathWanderer.

Do you wish to complain?

MathWanderer

What makes you think I am about to complain?

Ted Shifrin

Most of the comments on Amazon and Barnes & Noble are complaints that the book is too hard. :)

Mike Miller

Well, they're terrible books, so it's only natural.

:D

MathWanderer

I have nothing to complain at this point

Ted Shifrin

@MikeM: God knows Balarka still doesn't know any multivariable calculus/analysis.

Mike Miller

12:29 AM

Depends on the day.

Ted Shifrin

LOL, ok, @MathWanderer.

If you can do the medium and hard exercises in that book, @MathWanderer, you're doing very well.

MathWanderer

@TedShifrin Your book does contain insane problems but I thought the book is not difficult

Ted Shifrin

Oh, you have no idea what insane problems are :D

MathWanderer

Although I read Hoffman/Kunze's Linear Algebra first, which I thought was a good prep.

Ted Shifrin

That's a more advanced book than ours.

It's meant for junior-level math majors. Ours is meant for sophomores who know no linear algebra.

MathWanderer

12:31 AM

Well, different approaches help me

Ted Shifrin

Ordinarily, I would say to do their book after. But, whatever ...

MathWanderer

I need to review linear algebra before going to Lang's Algebra and Hungerford's Algebra in-depth

I started with H/K first since I got it for gift

Ted Shifrin

Lang is absurd unless you're a very sophisticated graduate student. Do Artin.

MathWanderer

So here is my story

my current research in the machine learning and topology, and their applications to biology introduced me to the algebra

And I got those books as a farewell gift from emeritus professor

Ted Shifrin

Gifts don't necessarily mean it's the right thing to do.

MathWanderer

12:33 AM

Of course

that was a reason why I have been searching for elementary books to complement them

Artin, Pinter, Herstein, etc.

Ted Shifrin

Look at Michael Artin's Algebra. You will know most of the linear algebra in there.

Forget Herstein. I don't know Pinter.

MathWanderer

Do you not like Herstein?

Ted Shifrin

No.

It treats algebra as symbol-pushing.

And tricks.

Artin truly shows how algebra fits inside unified mathematics.

MathWanderer

Ohhhh....I see...because I have his Topics in Algebra, which I never read.

Artin, I see.

I am probably going to sell Topics in Algebra and buy Artin

Ted Shifrin

(I have strong opinions. Many people do not agree with me.)

MathWanderer

12:36 AM

How do you think about Rudin's PMA, but the way?

by the way, I mean.

Mike Miller

Lang is a bad book with good exercises.

Ted Shifrin

I think it's a fine book for a strong student who can draw lots of his own pictures. But it's very hard for most students.

Rudin has excellent exercises, but professors who teach out of it and never draw pictures or provide motivation/illumination make it hopeless.

MathWanderer

That is why I like Pugh

But many of my friends swore by Rudin as a gateway to truth

Mike Miller

Well, I'm not a strong enough student to get anything out of it. The exercises were good qual prep.

Ted Shifrin

I don't know Pugh's book, but I know him very well. I took graduate courses from him. I expect his book is quite good.

smacks @MikeM

MathWanderer

12:37 AM

His book has many pictures. \

Ted Shifrin

Yes, he's very geometric in approach.

As you noted, I like pictures, too. Even my abstract algebra book has lots of pictures. :P

But I'm not recommending it to you.

Too low level.

MathWanderer

What is the name?

It might be helpful too

Ted Shifrin

Something like Abstract Algebra: A Geometric Approach.

I like "A Geometric Approach." Although I skipped it in my differential geometry text. :P

MathWanderer

It is written by you too!

Ted Shifrin

I said so, didn't I?

MathWanderer

12:40 AM

When you said "Even by abstract...", I thought you mean the books you have

Ted Shifrin

Oh, sorry about that.

MathWanderer

I should take a reading at that book too

On this Summer, I am exploring many branches

like algebra, representation theory, complex analysis, etc.

I could not resist my temptation and curiosity to get my brain to them

Ted Shifrin

Well, representation theory is linear algebra with a lot of group theory, so you need group theory first.

MathWanderer

That is also one of reason why I started to read Hungerford

Ted Shifrin

Complex analysis is beautiful stuff, but you shouldn't get too far removed from the material you need for your work.

MathWanderer

12:42 AM

Well, I will be doing a reading course in analytic number theory on August, so I need them

Ted Shifrin

Hmm, @Ali said he was asleep, but he is still here.

Yes, you do for that, @MathWanderer.

MathWanderer

But I found elementary books that I can finish within a month.

Ted Shifrin

LOL

MathWanderer

Jameson and Needham, I especially like first

Ted Shifrin

I don't know that.

MathWanderer

12:43 AM

It is very concise book, elementary exposition, and treat only few topics

Ted Shifrin

If you've been through Pugh or Rudin, you should do complex more seriously, but you can't devote that much time to everything.

MathWanderer

How "serious"? I won't be taking any course in complex until next Spring

I can only budget small amount of time for learning complex, so Jameson fits me

Ted Shifrin

Seems ridiculous to self-study and then take a course. Why not reorganize?

MathWanderer

Could you provide me advice?

Ted Shifrin

Just saying you should save complex for the course and wait for analytic number theory. You seem to be trying to learn everything.

MathWanderer

12:46 AM

Should I not pursue ANT then?

Ted Shifrin

Postpone until you've actually taken the complex analysis course. No need to do everything at once!

You should also prioritize a little bit according to your research area?

MathWanderer

My research area involves a lot of mathematics

Ted Shifrin

I would have expected more applied things.

Like dynamical systems/differential equations.

MathWanderer

Not really....

We try to apply topology to figure out better ML algorithms for data analysis

Ted Shifrin

I just can't see all the algebra, number theory. Topology, sure.

MathWanderer

12:48 AM

And algebra is needed since my collaborated work is on algorithm efficiency too

Ted Shifrin

I never knew that the theory of algorithms was so much abstract algebra.

MathWanderer

Me neither until my professor and collaborator told me

Ted Shifrin

LOL, ok, I'll trust you.

MathWanderer

Algebra though is used extensively in topological data analysis

as TDA is heavily depended on cohomological structures

Ted Shifrin

More homological algebra and algebraic topology. Not so much algebra per se.

MathWanderer

12:50 AM

Isn't algebraic topology need algebra?

My grammatical mistake, I am sorry about it.

Ted Shifrin

I'll let @MikeM answer that one. Don't go crazy with abstract algebra. But learn basics about groups, rings, modules.

Mike Miller

You should know some algebra.

MathWanderer

Thanks for the advice.

Mike Miller

You won't need the Sylow theorems, say.

MathWanderer

I see.

Ted Shifrin

12:52 AM

Or Galois theory, really.

MathWanderer

I see!

Ted Shifrin

The material in Artin on finitely generated modules over a Euclidean domain is important.

MathWanderer

Thanks for the information!

Right now, I am reviewing Rudin and reading Dugundji and Hungerford

but I should adjust my plan then

Ted Shifrin

Yikes @Dugundji.

MathWanderer

???

I love that book!

Ted Shifrin

12:53 AM

Although I sort of liked that book. It has mistakes.

It's way too much point-set topology.

MathWanderer

Yes, but I thought it makes an excellent intro. to topology.

Much better than Munkres or Willard books

Ted Shifrin

Overkill. If you know half of Munkres, you're fine.

MathWanderer

I did not read it

Ted Shifrin

Yet you know it's "better"?

MathWanderer

When I took gen. topology course on the last semester, which Munkreas was required, I read Dugundji

Ted Shifrin

12:54 AM

You are unlikely to need that much general topology, then. If you took a course, move on to other stuff.

MathWanderer

Thanks for the information. I was just doing some problems I was not able to figure out on the last semester.

I feel like if I cannot do every problem, I am done for

Ted Shifrin

No, relax!

MathWanderer

?

Mike Miller

I'm sure all the stuff about non-metrizable spaces is deeply relevant to topological data analysis :p

Ted Shifrin

@MikeM: Sarcasm may be lost on this audience.

MathWanderer

12:56 AM

But I feel stupid and incomplete when I could not finish the book from page one to last pne.

Ted Shifrin

@MathWanderer: Seriously, you do not need to be an expert on every single thing. Concentrate on basics that are truly relevant.

MathWanderer

@TedShifrin Thank you for the advice. How should I resist my temptation?

Whenever I tried to move on after not able to solve problems, I cannot think of nothing else...

Ted Shifrin

LOL. There's only so much time and so much mental energy.

MathWanderer

I also feel like everything in the books is important

Ted Shifrin

If a particular problem truly fascinates you, work on it.

I'm puzzled that after all this advanced stuff you find my book that challenging. Very few problems should be challenging compared to Dugundji, etc.

MathWanderer

12:58 AM

Your book is not challenging like others, but some problems do

Ted Shifrin

@MathWanderer: THis is why teachers provide some guidance to what's important and what's not. There's too much stuff in books.

MathWanderer

I see.

Ted Shifrin

OK, I'm leaving. Good luck, @MathWanderer. I know you'll do fine.

MathWanderer

Thanks, you too!

I am going back to my stuidy

Leaky Nun

3:47 AM

2k rep!

r9m

well done @LeakyNun ! :-) .. btw what exactly is a leaky nun? XD

Leaky Nun

@r9m anagram of my name

r9m

@LeakyNun I see :)

MathWanderer

6:28 AM

I love math!

Huy

ok

Balarka Sen

@TedShifrin Eh, I just spent a year on that :(

The Artist

Hey guys, I know this is a weird question to be asking here. But do you guys wash your new clothes before wearing?

Leaky Nun

@TheArtist Yes

Balarka Sen

I don't have new clothes

The Artist

6:41 AM

@LeakyNun what if it's winter time (no sun) and you don't have a dryer. Do you think I should wait days to dry off my clothes?

Leaky Nun

@TheArtist depends on whether you need the clothes quickly.

The Artist

@LeakyNun Hmmmm.

@BalarkaSen hehe

Huy

7:06 AM

@TheArtist wait days.

also, buy a dryer

you can also put them in your oven

(kids shouldn't try this)

Balarka Sen

great idea

The Artist

@Huy you can put in your oven, are u serious?

Balarka Sen

@Huy well, i don't know the point of this disclaimer in many places. when they tell you "kids, don't try this", don't they realize they're literally telling him to try this?

Huy

@BalarkaSen: maybe that's the point ;)

@TheArtist: if you're experienced, sure. or you can hang them up right next to it and open the oven and use the warm air to dry your clothes

you just shouldn't set your oven to like 550°F and then leave the flat for 2 hours

Balarka Sen

@Huy devil: "even i couldn't have put it better"

Huy

7:09 AM

=)

Balarka Sen

Hmm, I just had an idea about something I wanted to prove. Now let's hope it works.

Leaky Nun

@BalarkaSen what is it you want to prove?

Huy

that an oven is a safe environment for clothes

Balarka Sen

Something about self-intersection and normal bundles.

Huy

maths, really? boring.

Leaky Nun

7:16 AM

@BalarkaSen never mind

Abhishek Bhatia

7:33 AM

hi guys!

I asked this question a while ago. math.stackexchange.com/q/1819207/200649

If possible please have a look. :)

The Artist

@Huy Does it work with microwave ovens?

Axoren

@AbhishekBhatia The PDF of the $Uniform(0, 1)$ is equal to $1$ everywhere between $0$ and $1$.

This is the definition of the Uniform Distribution.

Abhishek Bhatia

@Axoren how?

Axoren

$f_U(u) = 1$ always, it doesn't matter what kind of expected value you're calculating.

This is the definition of the Uniform.

Every point in the interval $[0, 1]$ has equal probability, but there are so many points that each of them would have probability of "essentially" $0$.

So, instead, we talk about them as a probability density around the point.

The probability density is $f_U(u) = 1$

Abhishek Bhatia

That makes sense, but how can it be 1.

Axoren

7:43 AM

You seem to be having an issue with the definition of the $Uniform(0, 1)$ distribution. Why do you think can't it be $1$?

Abhishek Bhatia

That means each very small interval around x has probability 1.

Axoren

You're still confusing topics.

Once you're in a continuous distribution, you can't talk about probability in the same way anymore.

Huy

@TheArtist do you understand what a microwave does?

Axoren

Every point has a probability of $0$, there are more than $\omega$ points on any real number interval.

There are just too many points to ever assign all the points in an interval with a non-zero probability.

So, instead, we work with densities.

Consider $g(u) = P(U < [0, u])$

The Artist

@Huy boils water in the food?

Axoren

7:47 AM

$g(u)$ is the cumulative distribution function of $U$, where $U$ is the $Uniform(0, 1)$.

$g(0.5) = 50% = 0.5$, because we know that half of the points are in the interval $[0, 0.5]$, so there's a 50% chance of being in that subinterval.

@AbhishekBhatia Do you agree with that?

What you'll notice is that for $u \in [0, 1]$, $g(u) = u$.

We know that the probability function is the derivative of the cumulative distribution function.

So what happens when you take the derivative of $g(u)$ with respect to $u$?

$f_U(u) = g'(u) = 1$

Abhishek Bhatia

Just watching the lecture again, will get back and read your comments in 10 mins. :)

Axoren

@AbhishekBhatia I may not be here in 10 minutes, so I'll leave a little bit extra for you when you return.

Good luck with this stuff, it's not trivial to the uninitiated or even the initiated.

So, the remarkable thing is that if we take infinitesimal steps along the interval, we notice a non-zero shift in the cumulative distribution function.

And that the shift is of slope $1$.

What we've actually done is shown that for every $dx$-wide neighborhood about a point $x$, we have probability $dx$ of hitting it.

So, we can say that it's density is $\frac {dx}{dx} = 1$.

Abhishek Bhatia

8:13 AM

@Axoren Thanks!!, makes sense now. The probability is $dx$, I thinking it of be 1. Also you're earlier points made it clear. If you can post an answer I will accept it.

xpmrz

Does the center of mass of a rod divide the rod into to 2 pieces of equal mass?

Leaky Nun

8:46 AM

@xpmrz not necessarily

Imagine a rod of the density of a blackhole is attached with another rod of the same mass. The center of mass would not be the point where they attach

Huy

@TheArtist: and do you know how a drying machine works?

Mithlesh Upadhyay

Is the answer? math.stackexchange.com/questions/2969/…

Mithlesh Upadhyay

9:55 AM

Where(like room) should I put the my review - bad post to close or delete ?

Is the answer math.stackexchange.com/questions/970187/…

Is the answer? math.stackexchange.com/questions/970187/…

Martin Sleziak

@MithleshUpadhyay I guess it is usually enough that you review the post, we would be swamped in chat. The room which is the most closely related to flagging is C-R-U-D-E. However, it is rather inactive lately - there are not many users who come there.

in C.R.U.D.E., 2 days ago, by Martin Sleziak

This room now has much less activity than it used to have. For example, if you look at January 2015, there were several users relatively active in this room.

BTW if you think that for some reason it is useful for other users to see the review, there is already complete history shown for users with access to the review queue. (One list per review type, link can be easily seen if you are the review queue.)

And history of review by a specific user is shown in the profile.

Mithlesh Upadhyay

@MartinSleziak, Thanks.

Leaky Nun

10:11 AM

Is the Gamma function the only continuation of the factorial function that is smooth to every degree?

i.e. continuous at every derivative

Also, how is it derived?

Balarka Sen

10:32 AM

@LeakyNun No, it's not the unique extension of the factorial function which is complex analytic. However, with mild condition, it becomes unique such.

IIRC it's called Bohr-Mollerup's theorem.

Leaky Nun

@BalarkaSen Sorry I don't understand "mild condition"

Balarka Sen

You need to impose some extra conditions. Then $\Gamma$ does indeed become a unique complex analytic extension of factorial.

Leaky Nun

what are those conditions?

And for all intends and purposes, I mentioned the condition "smooth to every degree"

Balarka Sen

I don't remember it anymore: I just gave you the name of the theorem, you should google it.

Leaky Nun

is that a valid defining condition?

prodprod

10:34 AM

the extra condition is log-convexity, i believe

Balarka Sen

I don't understand what "smooth to every degree means". Do you mean infinitely differentiable?

Leaky Nun

> Bohr-Mollerup Theorem. Γ(x) is the only function that satisfies f (x + 1) = x f (x) with log( f (x)) convex and also with f (1) = 1.

@BalarkaSen yes.

Balarka Sen

Being analytic is stronger than being infinitely differentiable.

Namely, you should also require it admits a Taylor series at every point.

Leaky Nun

I see

but the theorem does not include this condition.

is this condition alone uniquely defining?

Balarka Sen

@LeakyNun Mmm, I see. I forgot how surprising the theorem is: it doesn't even assume the function is differentiable :)

@LeakyNun What do you mean?

Leaky Nun

10:38 AM

My question is, can I define another function which is an extension of the factorial, and is analytic, uniquely?

Well... is gamma analytic? also, what is its taylor series?

Balarka Sen

@LeakyNun Yes, there are quite a few analytic functions which extend the factorial. Google may tell you some.

Yes of course the gamma function is complex analytic.

Leaky Nun

what is its taylor series?

Balarka Sen

There's a wikipedia page on the gamma function, you know :P You'll find all your answers there.

Leaky Nun

$f(z)=\Gamma(z)+\sin(\pi z)$ :o

Balarka Sen

Here is a function which is complex analytic and extends the factorial, but is clearly not the gamma function.

Or that, sure.

Leaky Nun

10:43 AM

nice.

@BalarkaSen I can only find the taylor series of ln(1+Gamma)

Balarka Sen

I can see Laurent expansions written out in many places.

You can't find a globally defined Taylor series because $\Gamma$ is not entire: it's complex analytic away from the negative numbers, iirc.

Leaky Nun

Oh, sorry

Balarka Sen

I am no expert on gamma function though, so I am not the ideal person to ask about what they do or don't.

I just know a bit of complex analysis.

Leaky Nun

I see

Ali Caglayan

@TedShifrin I went to bed with my laptop open

Balarka Sen

10:59 AM

Hello again.

I want to jump into the next section in Guillemin-Pollack but I am not sure if I remember everything from the previous ones.

By remember I really mean understand

Mike Miller

11:22 AM

athr4 qe3q

Huy

that's my password

Balarka Sen

how do you even remember it

Huy

I just ask Mike whenever I forget it

Leaky Nun

11:50 AM

To anyone who understands information theory and security and is in an infuriating argument with someone who does not (possibly involving mixed case), I sincerely apologize.

spread the word

Danu

Hi guys @MikeMiller @BalarkaSen @Huy

and @Andrew

Hidee ho.

Hellu everyone.

How's life?

Is cool. Trying to learn math. And you?

Huy

11:55 AM

hi @Danu

Danu

@AndrewThompson Going through another round of doubts whether I want to switch to math or not :\

Balarka Sen

Toss a coin.

Andrew Thompson

@Danu You study physics IIRC?

Danu

@AndrewThompson Yep

Andrew Thompson

@Danu Okay, so there are pros and cons for staying with physics:

Pros: You can appeal to muggles by pretending being friends with you will be just like in The Big Bang Theory.

Cons: It's physics.

Transcript for

$Mathematics$ Mathematics