There are not that many theorems, but I never reallya bsorbed them.

Lang's treatment of Galois theory is deep.

Hard to say know, @Mike. But I've had a pass at it twice, and had it decently well the second time.

it discusses both a brute force way---the one I know how to do---and something far more subtle involving Jacobian ideals and hypercohomology

which, um, i really never got

It's been a year and a half since I've touched it, but I'm pretty familiar with many of the results and standard type problems.

Is logic a big field today?

it was all far far above my head, alas.

no, Jasper

I guess solving P vs NP would be good.

i'd classify P v. NP under theoretical computer science, i guess

Are you so sure, @Ted? I guess you're not including set theory as part of logic?

If you can create an AI that can speak in natural language fluently, you could make big bucks

sure I am

@Semiclassical Which like theoretical physics, is math, lol

hah.

how many top departments in the country have large logic groups? only a small handful.

Anything with theoretical in it has no practical applications, lol.

ehhhh, no

Theorical applied maths

condensed matter theory has been tremendously applicable to the real world

for example

not in the sense of quantum computing or anything as speculative as that, to be sure

@Semiclassical Do you think you will ever reach a stage where you consider yourself "well" from your mental problems?

but in the straightforward sense of "understanding this physics in sufficient precision as to make better technology", it's tremendously relevant

eh, I guess i don't frame it like that

I was trying to watch a youtube video series on quantum entanglement, and I just. could. not.

i frame it more as just trying to figure out what's the next step, and where i can grow

It was so boring, the lecturer took 10 minutes to try to explain bra-kets, and did a terrible job of it.

Ah OK. For me, I frame it as "well".

and not in terms of some destination that i can't conceive of

we have bad lecturers everywhere, @David, even on youtube

For me, there is a state I can conceive of, that is attainable, but I just have not attained it due to the various difficulties.

I really wanted to know more about the difference between cbits and qbits, but I couldn't wade though his terrible explanation of vectors and stuff

LOL ... you could only imagine how he'd do on the harder stuff?

A mosquito is a vector.

sometimes people explain hard stuff better than easy stuff ... they think more about how to do the hard stuff.

of disease! (rimshot)

a person getting a shot is a tense-or.

That's how you explain vectors to freshmen.

smacks Semiclassical

Mosquitoes like freshmen because their blood is fresh.

not I, Jasper

Twin vectors live in dual spaces.

Who's ʙᴀᴅᴀᴛᴍᴀᴛʜ ? (his previous username)

and a gymnast is both a spin-or and a twist-or

@Hippalectryon user130018=Bart

= mr eyeglasses

LOL

Only you call him that

=nabla blah

are you saying I don't matter, Jasper?

it's annoying that some people need a dozen names

ahem

Is an ermine-wearing cow on the Alpine slopes a Minkowskian?

smacks @David

I think it's time for me to go cook dinner.

Le appetite.

Au revoir, @Ted :)

À bientôt, @Alex.

@alex Are you learning French or German or Russian for the language exams?

@ABeautifulMind: well, that's a ways off. :) But probably French.

Ah OK. Ted knows all three, LOL.

Pasta la vista

I was taught French many years ago. But I can only read it now.

MIT has CHinese as well, which I know. =)

@DavidWheeler O_o

I think CHinese will become the next big language in mathematics.

@ABeautifulMind le wut

@Hippalectryon I mean, after Eng, Fre, Ger and Rus.

Ah ok

I speak CHinese.

And I have typed H instead of h thrice, LOL.

Je ne peux ni lire ni ecrire le Francais

th rice

Sort of funny story. Some time back, Go Yamashita was holding a seminar on Mochizuki's most recent work. I was curious about it, but the description was in Japanese. I'd taken Japanese, but only for a year and a half, so I couldn't get very far.

@DavidWheeler Je vois ça

I asked my brother (who knows very little advanced math) to translate as best as he could for me, since he's essentially fluent in Japanese. He told me the description was saying something about "skim" theory.

Haha. Mathematical lang is quite diff from real lang.

I was really confused but thought for a minute and realized he was talking about "SCHEME" theory. Lol :)

I have no idea what skim refers to.

Oh, LOL>

Is that your dog @alex?

Sadly not, @ABeautifulMind. Just a cute dog that my friend insisted I make my avatar, lol.

Ce n'est pas vrai.... bah, je m'en fous :(

Considering this is a Sun there, this chat room is quite busy.

Le hello again. @Ted I still don't understand what the "le" is for. I just wanted to say that I got my answer for the question we discussed earlier. But I will have to go home and type it up or write it out and the take a picture and send it to you.

One day, when the sun burns out, we will all die.

And I will be back home in like 2.5 hours

@JulianRachman It's a private joke I think.

@Ted ^^

Julian, Ted just left.

I don't plan on living that long

@ABeautifulMind oh. Lol.

Anyway, I believe in the big crunch theory. Infinitely many cycles of universe expansion and contraction.

On the plus side, most inhabitants of the Earth should be incinerated when the sun goes through its giant phase

@Alex NOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO‌​OOOOOOOO

@JulianRachman vador much ?

Lol. I'm sure he'll be back later. :)

And you know what, this universe expansion and contraction is mentioned in the Buddhist texts long ago before scientists talked about it.

Anyhoo, I'm off for now. Later, friends.

later pal

@ABeautifulMind Iono...I kind of like the directionality of time deriving from total history

la journée s'est assombrie

It's breakfast time. My mum will cook some noodles for me.

Why do so many people speak French q_q

Ju'n say pah

@Hippalectryon I speak Spanish English and some Chinese and French :)

I speek Merkan, with a smidge of wtf

Lol. I can't speak wtf. That is pretty impressive.

Can you teach me?

No, it's against the rules

OK.

:(

Soz

Lol I'll search for it on edX or OpenCourseware

'I gawd, Woodrow, I'm bort as hail

Lol

How can you be bort?

whajew say we go down Messico way and russel up sum steers

I don't know what that means but why not.

And lighten up on the drinks will Ya?

"I gawd, Woodrow, why duntye jus plant me n be dun wifit?

Fine sure. We be dun

I want to write a book on group theory

The first chapter is giving me trouble

Cool. Make the first chapter about the motivation for it leading up to group theory. That's what i would do

My problem is this-if you want to talk about groups intelligently, you need a small bit of set theory, mostly for concise terminology

Then write set theory your way in the intro and go from there.

Like munkres has a section for set theory and terminology in the first chapter

See, most people are afraid of groups, because they think "abstract = hard"

Then make it not hard :)

I think groups are super-easy-much more so, than say, calculus, or linear algebra

I ate two raw eggs.

Someday, I want to write a book called "Linear Algebra done wrong"

@DavidWheeler There is already one.

LOL

OK. So make a preliminary chapter discussing how you want readers to think and the set terminology and notation that you will be using throughout the book and then go through a short breakdown of set theory "your way"

@ABeautifulMind you crazy?

@JulianRachman It is true.

Why? :/

The first sentence: "A vector space is a field homomorphism into the ring of endomorphisms of an abelian group"

You were like "I'm hungry"

@David so you expect your readers to know that right? Then write that in your "words to reader"

What kind of status do you want the reader to be in

@JulianRachman then I want to introduce determinants ASAP....eventually (in the latter parts) I may get around to talking about bases. Maybe a small appendix where I mention matrices.

Ya. Maybe. Put that in the intro.

basically do things backwards-most linear algebra courses go on and on about matrices and row-reduction. ugh!

BTW, how do you go about creating a book on math without ending up copying someone else's book.

don't. peek.

Lol I can turn my notes into a book

Do you guys know what Real Induction is?

@columbus8myhw I have heard of it

basically you use sup's or inf's instead of successorship

Sort of?

So, if ordinary induction, you say a set $S\in\mathbb N$ is _inductive if:

ya ya

@David I can turn all my notes in successive order into a book. All my defn are original unless they are trivial

(Whoops. how do you make a subset sign?)

\subset

\subseteq or \subset

And then you know that if $S$ is inductive, then $S=\mathbb N$. Right?

So, with real induction, we have something similar.

Let's say $S\subset[0,1]$.

It's inductive if:

1) $0\in S$

and $[0,b) \subseteq S \implies b \in S$

2) If $x\ne 1$, then if $x\in S$, there is a $y>x$ such that $[x,y]\subset S$

3) $[0,x)\subset S\implies x\in S$

Here is a good paper on this.