Gonna share a series of Reddit comments of mine that I put too much effort into writing:

https://www.reddit.com/r/3Blue1Brown/comments/96d1zg/video_proposal_galois_theo‌​ry_and_group_theory/e40x4pj/

what are these shapes called?

Small

Sorry! I couldn't help it.

lol

they look like little candies or something

The description for MathOverflow is "MathOverflow is a question and answer site for professional mathematicians.". I understand that as that it's for people who at least have started a PhD in mathematics.

I don't know. Anyone?

@OskarTegby Sounds right

(Question 3 of my first comment might be hard for someone who doesn't know about GCDs with polynomials)

(in the link I just posted)

@geocalc33 Where is this from?

If it's from graphing a random-ish equation there's a good change it doesn't have a name

*chance

DogAteMy!!

@Ted I think I get it. Thanks!

Okey dokey, @Oskar :)

@Ted If I remember correctly, you are a professor in differential geometry. Right?

well, I was. Now I'm retired :)

Cool! Are you still doing math for fun? Like doing research or going into new fields.

Hi @TedShifrin! Also if you don't mind me asking - how did you keep up with what's going on with math when so many things are happening?

nah ... just miss the teaching some :)

hi @user31415

I didn't keep up with everything, that's for sure. I went to colloquium lectures pretty much every time I could. And seminar talks in my own field(s).

Seems like many valuable things are not written down though - talks are generally on things that are completed and are usually done a while ago

Do you still mostly rely on reading papers/talks in that case?

Not necessarily .... conference talks and colloquium talks are often given by people doing the work as it is happening ...

I really feel like the teaching of mathematics in general is so bad. At least when I see content from sources like 3Blue1Brown. Like, that presentation of Fourier analysis made it seems so obvious how it all worked. When I was taught it, they just talked about the properties of the machinery, not really describing it in a natural way.

Hm cool - thanks.

Different people like different styles of teaching, @Oskar. A number of my students loved mine, but there were some who hated it (and a few who hated me) :D

Hey!

Check out a thing I spent waay too much time writing

https://www.reddit.com/r/3Blue1Brown/comments/96d1zg/video_proposal_galois_theo‌​ry_and_group_theory/e40x4pj/

Heya DogAteMy ... we've missed ya.

(In response to somebody saying 3Blue1Brown should make a Galois theory video)

Yeah! Maybe you're right, Ted.

Is 3Blue1Brown an expert in everything?

I know nothing about that.

He makes animated math videos

No. He's just very popular because of his way of explaining mathematics and how beautifully he animates it.

I've never cultivated that skill ...

I don't know if he knows Galois theory but I feel like he probably does?

I think that his YouTube video on the Fourier transform is the best example.

I'm definitely a 20th century math teacher :P

Have you seen his series on linear algebra? It's pretty good

I think that most are.

I haven't. I will look. I should watch them all.

(It doesn't go in-depth but it's an overview)

I did try to use Mathematica interactively a bit in class (particularly diff geo), but it really disrupted the flow (pun intended) of the class ...

@OskarTegby This is true

Essence of Linear Algebra

So, DogAteMy, how's your year in Israel going?

It's going good so far!

I cooked stuff and didn't burn the dorm down, and it tasted good each time, so that's good

The Hebrew classes are useful

(Why are the verbs so hard)

Well, I guess that's good. What else are you taking?

Right now just Hebrew language courses

Ah.

Soon I go to Eretz HaTzvi (a yeshiva in Jerusalem) and take some math classes at a nearby university

(The Technion thing got cancelled, don't remember if I told you that)

(Not enough people signed up for their gap year program, so the program no longer exists.)

no, you didn't fill me in on stuff

Is it worth the time to learn graphics in LaTeX? I've just seen the PGF-manual, but is there no more approachable method of doing it?

I've never messed with it.

Most of the graphics capability I need far exceeds LaTeX's abilities. I use Mathematica and Adobe Illustrator.

Granted, those aren't free.

I wouldn't know.

There's always the "scan a piece of paper" option

Um, that's so 19th century, DogAteMy.

I'm currently doing the trial of Mathematica, but I don't know what to do with it. I feel like it requires more time than it saves.

@OskarTegby is Tikz not sufficient?

@Oskar: If you go to my webpage [linked in my profile] I wrote a basic primer on stuff in Mathematica for my diff geo students. You might find it slightly useful. It's short.

There's a high learning curve for Mathematica, but it's extremely powerful.

Alright!

I see that you're located in San Diego. I'm actually currently considering to go on exchange to the US, and actually California in particular. I have a major problem with the winter here in Sweden. I hate the darkness and cold.

Well, be prepared for drought and fires here :(

The other caveat would be that the great universities are overrun with students, so upper level math classes at Berkeley and UCSD often have 150 math majors in them :(

There's always people from California who go to the northeast for university, and they always regret it when winter comes

I loved being in New England during high school, college, and postdoc. But I couldn't take the weather now.

(braces self for New Haven winter even though it's the same in New York)

It's a bit harsher in New Haven, DogAteMy. You aren't in a concrete jungle there.

So it's actually not dark the entire days in winter?

True

Is it true that it's like around 70 most of the year?

Nope, @Oskar. It's still light 8-10 hours.

Depends where, @Oskar.

That sounds like a dream.

I've lived in Sweden too long.

San Diego is 60-80 most of the year, except now we're in a serious heat wave. Not that there's climate change or global warming. Those are just liberal rumors.

Okay, but you at least don't get like 40.

Really?

Isn't Sweden having a heat wave now?

Yes

All of Europe is having a horrendous heat wave ... Again, more liberal rumors.

Yeah! My friend from Florida has whined constantly about the lack of AC.

Haha! Okay. Now I get it. I got a bit worried there for a while.

As well he should!

I finally turned on AC a few days ago here. For the 3+ years I've been here, I've used it a total of 8 days or so.

It has been like 90 all of July.

It's subsiding now though, at least in Stockholm

I've almost never experienced a day of it being 90 in Sweden.

Incidentally:

Goes into more detail than just "global warming" (though that is a part of it)

He also had a video for the brutal cold we had in the winter

The NY Times Magazine had a thorough article on Sunday about the hearings on global warming back in the late 70s and early 80s. And how no one did anything. Should I link to it?

Sure!

(Here)

I'm looking at the video. I only see vector fields.

OK, give me a minute.

Here's the NY Times link.

Thanks!

Anyhow, @Oskar, let me know if you're gonna end up in my neck of the woods :)

@TedShifrin

how could this question be improved if you don't mind taking a quick look

I most certainly will, @Ted!

what isn't clear about it

Good video, @Akiva. Thanks for sharing!

@geocalc: Robert Bryant is the man in differential geometry. His comment is pretty much the point.

I thought that you were the man, Ted. ;)

Nope. Robert and I have been friends since grad school. He's a super-star.

@geocalc: The problem with posting on MO as opposed to MSE is that questioners are presumed to have a lot of background and expertise.

The few times I've posted on MO, I've made sure to have actual sources that I've cited and a question that seems 'research-level'.

I've only answered a few on MO. Of course, I've never posted questions on MSE, either.

I feel that the answer (and possibly the comments I made earlier) give a complete answer to your question.

Ben Crowell's answer is pretty much what I would have done. Solve the usual circle first, and then change coordinates. But Robert's comment about smoothness issues is totally to the point.

@Ted But stick to the top right quadrant and it makes sense.

open quadrant? yeah

Mike, are the math major classes at UCLA so obscenely yuge too (like Berkeley and UCSD)?

40 students

Oh, that's not unreasonable. There are some at UCSD that are 150+ ... Crazy.

If education weren't free I'd never stay in Sweden.

Closed quadrant seems ok as long as you don't want to continue past

Can't you go anywhere in the EU, Oskar?

I thought that was one of the whole points.

I guess that I could. Maybe, I shouldn't complain, but try to change things instead.

Going somewhere in California is a part of that plan.

Be warned about expense levels ...

I've heard. I just need it to be warm and have a university where the students are invested in their education than here.

Hey everyone

Hey @TedShifrin :)

I was thinking about UT Austin.

Ah, not California. Quite warm in Texas.

hi @Perturb

@TedShifrin I'm thinking of applying to universities in the US in around a year or two, do you have any general advice that would be useful to know?

I guess.

I can't access the Mathematica link on your webpage, @Ted.

You can chat with Mike and people like Demonark and Eric who'll be going through the grad school process.

Whoa, @Oskar. Let me double-check. You found it?

Hmmm, it works for me, @Oskar. Asks if I want to open it with Mathematica.

I get that.

Oh, and then what?

I do as instructed, but to no avail.

Hmm, it works perfectly for me.

Okay thanks @TedShifrin I know I'm probably not really at the same level as US undergrad students (in the same year as me) at the moment, but I'm trying to get up to the same level

Maybe try saving it to your hard disk and then open from Mathematica, @Oskar.

@Perturbative: Don't assume most US undergrads are at the level of folks you see in here.

Saving what to my hard disk?

That file, @Oskar.

Oh! Never mind!

Yeah! Sorry.

There you go! Now it works. Thanks!

Cool :)

Really? @TedShifrin If you don't mind me asking what are the standard US undergrads like? I assumed those that go onto top grad schools know most of the graduate level stuff already

Nooooo ...

True of lots of the students at Harvard, MIT, Chicago, etc., but far from true everywhere.

But to get supported as a foreign student you have to be pretty good ...

Pretty good with respect to my US counterparts I'm assuming?

Yeah.

At least you are a native English speaker ...

Of course, I'm out of the loop these days. But my suspicion is that the Trompolini presidency has decreased the desire of foreign students to come to the US for grad work.

@OskarTegby You are wrong to think everyone cares about the schoolwork.

And for students from certain countries it's become impossible.

At more prestigious university, @Mike?

Oh, @Oskar, I just saw you're now working on your masters.

universities*

I thought you were talking about coming for a year as an undergraduate.

If you don't mind me asking what would you say would be 'pretty good' for me trying to apply to a good grad school in the US? Like say I did a decent bachelors thesis in some cool topic in algebraic topology and have near 100% grades in analysis and algebra and that kinda stuff, and know some graduate level differential geometry/diff topology/commutative algebra/category theory etc, would you say that would be a good starting point?

You're talking about PhD?

I was talking about coming a semester or year in my master.

@Perturbative: I can't answer things like that. It depends on GREs, recommendation letters, grades, etc.

Okay, thanks for the advice @TedShifrin :)

Oh, @Oskar. I didn't think that sort of exchange program happened. I never heard of it.

Really? I'll have to look it up.

Maybe @MikeM knows of it ...