Mathematics - 2018-09-27 (page 4 of 5)

mercio

7:00 PM

both ?

Oskar Tegby

Only $f(Y)$

Prashin Jeevaganth

@Semiclassical Oh actually I just saw how you pieced everything together and you have a direct counterexample on the quantifier

mercio

so can $f(X)$ be $\Bbb R$, $f(Y)$ be $\{0\}$ and $f$ separate $X-c$ and $Y$ ?

Oskar Tegby

No.

mercio

so ?

Oskar Tegby

7:02 PM

It doesn't separate $X-c$ from $Y$.

mercio

so what is the only possiiblity for $f(X)$ and $f(Y)$ if $f$ wants to separate $X-c$ and $Y$ ?

Oskar Tegby

$f(X)>b+f(c)$ and $f(Y)<b$?

Both have to be $\Bbb{R}$.

mercio

No I am asking which of the following 4 possibilities allow $f$ to separate $X-c$ and $Y$
1. $f(X) = \Bbb R$ and $f(Y) = \Bbb R$
2. $f(X) = \Bbb R$ and $f(Y) = \{0\}$
3. $f(X) = \{0\}$ and $f(Y) = \Bbb R$
4. $f(X) = \{0\}$ and $f(Y) = \{0\}$.

Oskar Tegby

1

mercio

so you think you can find a $b$ such that $\Bbb R - f(c) > b > \Bbb R$ ?

Martin Svanberg

7:09 PM

How can I show that a commutative ring $R$ has a unique prime ideal $\implies$ every nonunit is nilpotent? Without using the fact that the nilradical is the intersection of all prime ideals. I can easily show that every nilpotent element $x$ is contained in the prime ideal, but not the converse.

Oskar Tegby

2

No.

mercio

same question about $\Bbb R - f(c) > b$

Oskar Tegby

It can't be done right?

mercio

it can

well

you can't rule out possibility 4 yet

Oskar Tegby

Didn't I propose that already?

mercio

7:10 PM

when ?

Oskar Tegby

11 mins ago, by mercio

what must $f(X)$ and $f(Y)$ be ? (impossible is not an answer to what they have to be)

11 mins ago, by Oskar Tegby

0

mercio

yes then I asked if you meant both of them and you said no ?

Oskar Tegby

I doubted. Now I'm more certain.

mercio

okay

so that's actually a really strong deduction that we get there

that $X$ and $Y$ must both be in the kernel of $f$

Oskar Tegby

Yeah

mercio

7:12 PM

then you have to remember that $f$ is continuous and that the closure of $X+Y$ is the whole space

what does that say about $f$ ?

Oskar Tegby

It should be able to map the whole space.

mercio

we already know that $f$ is a linear map from $E$ to $\Bbb R$ yes

Oskar Tegby

I don't get what you're going for here.

mercio

we are going for $f = 0$

Oskar Tegby

Yeah. We already said that. Right?

mercio

7:15 PM

no

we only know $f(X) = 0$ and $f(Y) = 0$

Oskar Tegby

Right.

mercio

we want $f(E) = 0$

Oskar Tegby

But by linearity we have $f(X+Y)=0$ right?

mercio

yes

Oskar Tegby

$f(X)+f(Y)=f(X+Y)=0$

mercio

7:16 PM

uuuuuuh kinda

Oskar Tegby

Why only kinda?

mercio

it's just abuse of notation that makes me unseasy between $0$ and $\{0\}$

Oskar Tegby

Okay.

So we know that $f=0$.

mercio

no

Oskar Tegby

$f(E)=0?$

mercio

7:18 PM

yes but why ?

Oskar Tegby

As $\overline{X+Y}=E$

But we had only $X+Y$.

mercio

yes, and what about $f$ makes this step possible

continuity?

yes

Why?

7:19 PM

what do you know about kernel of continuous linear maps

what is the definition of a continuous function ?

Oskar Tegby

The kernel is closed, so is the preimage?

The inverse is open.

mercio

the kernel is closed is good for my first question

Oskar Tegby

Okay.

mercio

and we know the kernel contains $X+Y$ and that the closure of $X+Y$ is $E$

Oskar Tegby

Yeah.

mercio

7:23 PM

so the kernel has to be $E$, which means $f(E)=0$

Oskar Tegby

Yeah

mercio

and so there can't be a nonzero continuous linear functional separating $Y$ and $Z$

Oskar Tegby

Yeah

Are we done?

mercio

I think ?

Oskar Tegby

If it is zero, then it doesn't separate?

mercio

7:27 PM

if it is $0$ then its kernel is not an hyperplane

and a map sending everything to a single point isn't really useful to separate things

Oskar Tegby

Then it's the entire space as just shown.

No.

Okay.

Now I only have to do the last part. This one will be an all nighter.

Alessandro Codenotti

You can recycle quite a bit of what you've done already for the last part

Oskar Tegby

Sorry for taking so much time. I obviously really appreciate your effort.

Yeah! Shouldn't it be almost identical for $\ell^p$?

Ted Shifrin

Congrats @Oskar @mercio :)

mercio

I am tired all of a sudden

Oskar Tegby

7:30 PM

I feel like the worst when taking so much time. It's just very slow when we can only write things.

Ted Shifrin

LOL @mercio: Wait 'til you've taught 40+ years like me :P

mercio

;w;

Alessandro Codenotti

@OskarTegby Maybe, you tell me

Daminark

:0

mercio

I only really learn things when I am struggling

Ted Shifrin

7:31 PM

heya Demonark

Oskar Tegby

Same!

Semiclassical

it's funny to me at times how much stuff here could be explained more easily if there was a chalkboard

Oskar Tegby

I don't see why things should be different in $\ell^p$ here.

Alessandro Codenotti

Hi @Dami

Oskar Tegby

Yeah!

Ted Shifrin

7:32 PM

@Semiclassic: One of the reasons I'm really not a fan of distance learning.

Semiclassical

yeah

it has its uses, but

face-to-face interaction at a board is hard to compete with in terms of immediacy and flexibility

Oskar Tegby

It's good for some things. Elaborate explanations like these aren't what it's best for.

It's not as if it's easier to get hold of the professor, though.

Semiclassical

one thing I do like about here vs. offline is that you can go back and reread the transcript

Oskar Tegby

Yeah!

Ted Shifrin

And find all our mistakes? :P

Semiclassical

7:34 PM

pretty much, lol

you can make notes of offline conversations, of course, e.g. taking pictures of a blackboard

but it'll never capture everything, since there's just so much there to capture

Ted Shifrin

Since cell phones, more students started skipping taking notes and taking pictures of the blackboards. I am very skeptical.

Semiclassical

whereas the transcript is a more complete record, albeit of a much more narrow interaction

Oskar Tegby

Learning shouldn't be easy. Then it isn't learning.

Krijn

Heyall

Ted Shifrin

heya @Krijn

Oskar Tegby

7:37 PM

Does even anything change in $\ell^p$? I feel like it doesn't.

Ted Shifrin

Mathematics is no place for feelings. :D

Krijn

@TedShifrin I think this is because students are going from "knowing things" to "knowing where I can find things"

Semiclassical

eh

Ted Shifrin

(Dreads the starboard.)

Semiclassical

proof isn't a place for feelings

Oskar Tegby

7:39 PM

Although, I feel like everyone, understandably, is sick of me and my questions by now.

Ted Shifrin

@Krijn: It's a matter of understanding more than knowing, though, for serious mathematics.

Alessandro Codenotti

@TedShifrin I need to write things by hand to learn. Even if I'm studying from a book or notes by myself, I write a lot

Oskar Tegby

I need to try my hardest, and then discuss it with someone if I can't solve it myself.

Ted Shifrin

I agree, @Alessandro. When I studied for my graduate qualifying exams, there were some analysis proofs I wrote out a dozen times.

Semiclassical

@Krijn The version of that which I've seen in intro physics occurs most in the pre-med/bio major version of the course, though it's present in all versions

Krijn

7:40 PM

I agree as well, I don't ever read the notes I take, but I still take them

Semiclassical

namely, they tend to treat the problems as a matter of finding the right formula

Ted Shifrin

When I took algebra in 2nd year of college, I think I rewrote my notes every day.

I don't remember doing that for other courses.

Semiclassical

They rely on a very simple notion of pattern-matching

Oskar Tegby

It's fascinating how different we all are.

Jasper Loy

I never took any notes in college, lol.

Ted Shifrin

7:42 PM

I am very different from me.

Oskar Tegby

I am not me.

Semiclassical

And I think that reflects their coursework: They're required to absorb swathes of information and give the right response when asked about it

Ted Shifrin

Oh, I always took notes ... in college, grad school, some seminars in professional life.

Semiclassical

That doesn't work so well in intro physics, though, because the pattern-matching is at a bit deeper level

Ted Shifrin

@OskarTegby We'll just call you Sybil :)

Jasper Loy

7:42 PM

For my courses, I will just refer to the relevant books later on, if I do attend the lectures in the first place, lol.

Oskar Tegby

Haha why?

Semiclassical

what you need to be watching for are patterns of solution and application, not specific problems themselves

Ted Shifrin

A lot of us lecturers don't just read out of the textbook, though. Even using my own textbooks, I hardly ever followed (except for certain big proofs, where I tried to give more intuition and often reorganize).

Oskar Tegby

What's Sybil, @Ted?

Jasper Loy

I am sorry I haven't watched any of your videos yet @TedShifrin, even though I did click on some of them.

Ted Shifrin

7:44 PM

Sybil had something like 20 different personalities.

Semiclassical

Which Sybil?

Jasper Loy

Is that the movie Split?

Ted Shifrin

Sybil

Semiclassical

ah

Jasper Loy

In the movie Split, the guy had many personalities too, and he kidnapped three women.

Krijn

7:45 PM

@TedShifrin This should be a quote on the book. "Even I hardly follow this book" - Ted Shifrin, on his own book.

Semiclassical

of course, there's Sybil-the-character and Sybil-the-person

Ted Shifrin

oh, that's a new movie — I hadn't heard of it, Jasper.

Jasper Loy

Schizophrenia is not the same as split personality, but many people mix up the two.

Semiclassical

@TedShifrin it's an m night shyamylan picture

Ted Shifrin

@Krijn: I mean ... a lot of faculty literally transcribe the book to their notes and then their notes to the board. I make sure to do different examples almost all the time.

Semiclassical

7:46 PM

there's a sequel of sorts along the way, though the details of that are a spoiler

Oskar Tegby

Is the last part of the problem easy? I just want to go to bed, but I want to have it all done before then. :(

Jasper Loy

Even my schizophrenic friend is doing better than me. He is getting married this weekend.

Oskar Tegby

$E=\ell^p$ and $E=c_0$

Jasper Loy

Oh @Semiclassical I have stopped taking meds for a few months. I don't think I will ever take them again. Doesn't really help, it seems...

Daminark

Hey @Alessandro and @Ted!

Ted Shifrin

7:50 PM

So, how's alg top going, Demonark?

Jasper Loy

Does anyone here know of a book that treats axiomatic geometry in 3 dimensions in detail? Most books on axiomatic geometry do it in detail only for 2 dimensions.

Ted Shifrin

Since I hate axiomatics, I have no idea.

Daminark

I've had to pause it a bit, yesterday I flew into Chicago and today we're getting a couple things that I don't have, but hopefully we'll be done soon and I can kick it back up

Ted Shifrin

Didn't Euclid do a good deal in 3D?

Oskar Tegby

How can one not love all of math?

I think that people who don't like math are just lying to themselves.

They're insane.

Daminark

7:51 PM

Did all the exercises of 1.1 except for the plane cutting compact sets in half

Jasper Loy

Euclid is not rigorous enough for me. There are some mistakes in the axioms, something like that.

Ted Shifrin

The ham sandwich theorem is cool, Demonark, but I told you that nailing details takes time.

@Jasper: Sounds like you've never even read Euclid carefully.

Semiclassical

@JasperLoy i'm currently between clinics right now, and had convinced myself I was out of a med when I really wasn't. made it quite discombobulating when I asked the pharmacy and they told me I should still have a week left

Jasper Loy

@TedShifrin Yes, you are right, lol.

Daminark

Lol, that's a bit of a stretch. Like, I feel with most subjects people should be able to recognize what other people find interesting, but people have different taste.

Semiclassical

7:53 PM

(I had two bottles, one new and one old. I had started using the new one, but then accidently put it in the wrong place and went to the old one. so when that one ran out I was like wtf)

Daminark

And yeah you did mention. But yeah I backtracked and have been reading chapter 0 didn't quite do the exercises before my flight

Ted Shifrin

@Semiclassic: You're young to be so absent-minded :P

Semiclassical

lol

i am not an organized person

Jasper Loy

@Daminark You would love Bredon's Topology and Geometry if you are into algebraic topology.

Daminark

Is that an age thing? I was absent-minded even at 3

Ted Shifrin

7:54 PM

I am more organized than the average bear, I think.

Demonark: It tends to get worse with aging and the dying of neurons.

Not to mention Alzheimers ...

Jasper Loy

@Semiclassical Discombobulating is a difficult word for me.

Daminark

@JasperLoy I've been told it was pretty good, nice that it mixed difftop in

Semiclassical

i'll be honest, I had to look up the spelling

Jasper Loy

@Daminark Not exactly differential topology, but just differential manifold theory.

Daminark

Does it not have stuff like transversality and degree?

Jasper Loy

7:57 PM

Anyway @TedShifrin currently my first choice for a book on axiomatic geometry is ... John Lee's Axiomatic Geometry, lol.

Semiclassical

the fun thing is that discombobulate doesn't really have a proper etymology

Jasper Loy

@Daminark Only a little bit. It's not like Morris Hirsch's Differential Topology.

Krijn

@TedShifrin Let's not bring age and mathematics back together this week...\

Semiclassical

'"to upset, embarrass," 1834, discombobricate, American English, fanciful mock-Latin coinage of a type popular then"

Ted Shifrin

I just don't like teaching anything axiomatically. I mean, we all use basic axioms and logic, but I do not like the course we "train" future high school math teachers with. And high school geometry with its two-column proofs ruined math for generations and generations of students.

@Krijn: Are you turning aged this week or are you referring to global affairs?

Daminark

7:58 PM

Also when I get some more AT and do manifolds but more sophisticatedly I'd like to do more difftop. Neves is teaching grad this year so I wonder if he's gonna do forms this time for cohomology

Jasper Loy

I am interested in it for its own sake. I don't know why they bring in high school math teachers into the picture either.

Semiclassical

I still remember that my geometry book talked about 'paragraph proofs' only near the end of the book

aka how anyone actually doing math does proofs

Krijn

@TedShifrin The latter, I think, I'm not sure...

Jasper Loy

Actually, the 2 column proof is just a format. Who says we have to write it in 2 columns?

Daminark

Lol I remember going into college I was told that people who liked high school geometry would be in better shape for proof-based math and I was like yeah I didn't like that, probably not gonna do math

Semiclassical

8:00 PM

lol

Ted Shifrin

The teachers do.

Daminark

I anticipated at the time that I would do physics or chem

Then I took Spivak and was like nah this is way better

Jasper Loy

I don't see how high school geometry is related much to proof based math.

I think the simplest proof one can show high school kids is that root 2 is irrational.

Ted Shifrin

Oh, Demonark, I had numerous students in the Spivak course (and then, later, in my multivariable math course) who were shocked to discover math was interesting.

That proof is in Euclid, @Jasper, btw.

Semiclassical

I guess the logic is: Euclid is where we get plane geometry from, and Euclidean geometry was derived from Euclid's axioms, so let's make geometry the place to talk about proofs

Ted Shifrin

8:02 PM

They were very consumed with commensurability.

Alessandro Codenotti

Hi @Mathei

Jasper Loy

I wonder why Spivak never wrote his Calculus on Manifolds like his Calculus. Do you know @TedShifrin?

Daminark

@JasperLoy then show them one of the best proofs in the subject. Which is that a^b might be rational even if a and b are irrational

Ted Shifrin

he was barely out of grad school when he wrote Calculus on Manifolds.

Rithaniel

I like that statement: "shocked to discover math was interesting"

MatheinBoulomenos

8:02 PM

Hi @Alessandro @Ted @Daminark and everyone else

Ted Shifrin

I mean it, @Rithaniel.

heya @Mathein

Semiclassical

I think the key for me was that I made math interesting for myself

Jasper Loy

@Rithaniel looks like @MikeMiller I suspect they are the same person lol

Semiclassical

like, I did a good deal of playing around with simple number theory stuff in high school, without actual expertise

Rithaniel

Yeah, I agree. I still find the statement mildly humorous.

Jasper Loy

8:04 PM

For once someone actually agrees with me.

Ted Shifrin

Math is ruined by most primary/secondary teaching.

Semiclassical

so for instance I didn't have a good way to explain why a number and its digital sum were the same mod 9

i knew, for instance, that 10^n = 1 mod 9

Rithaniel

Well, not always. Sometimes you do get a few good primary level math teachers.

Jasper Loy

@Semiclassical I call digital root the final one digit number.

Rithaniel

It's uncommon, but it does happen.

Semiclassical

8:05 PM

but my way of explaining it would be based on the binomial expansion of (1+9)^n

Daminark

Oh actually NT was something I liked even in high school. If I give credit to the IB for nothing else, they have a project that they ask people to do. Mine was on like, in-the-womb-level modular arithmetic but I still liked it a lot

Semiclassical

which is overkill

Daminark

Hey @Mathein, how's it going?

Semiclassical

my finest accomplishment was coming up with a division rule for 7s, based on 100 = 2 mod 7

Oskar Tegby

@Ted: Things should be quite similar for $E=c_0$. Right?

Jasper Loy

8:06 PM

@Semiclassical 7 and 13 is hard. You must be genius.

Semiclassical

it was a task, I'll say that much

Jasper Loy

I can at most figure out 10 myself, lol.

Semiclassical

though, the fact that 100 = -4 mod 13 may help

Maximus

Hello is there a quick way to explain to someone why Z_2 is isomorphic to GF(2)? Basically Z_2 is a field and GF(2) is a field with 2 elements.

Semiclassical

i dunno. with seven it was nice since you had 100 = 2 mod 7, 100^2 = 2^2=4 mod 7, 100^3 = 2^3=1 mod 7

MatheinBoulomenos

8:08 PM

@Daminark pretty well, thanks! I went on a trip to the hut in which Heidegger wrote being and time with a friend who's a philosophy major, that was fun. And for you?

Semiclassical

with 13 you'd have nothing so nice

Jasper Loy

First time I see semi discussing congruences.

Semiclassical

@Maximus i'm not sure what you're looking for beyond "show that the isomorphism works"

Jasper Loy

foreverinactive seems to be gone from the site for now.

Semiclassical

i.e. show that there's a bijection which preserves the field operations

Maximus

8:11 PM

@Semiclassical I see but isn't Z_2 just GF(2) in different notation?

Semiclassical

sure, but you can say the same about any isomorphism

Maximus

my book says the field Z_p is denoted by GF(p), so that's what confuses me. how do the elements in GF(p) look like?

Semiclassical

I'd just take them to be integers 0,1,...,p-1

Krijn

That does make most sense

Maximus

I see, so it just means the same thing

Semiclassical

8:15 PM

they're saying that GF(p) is just a different name for Z_p

Maximus

right

Krijn

But there is only one field of a certain finite size up to isomorphism

Semiclassical

dunno why they bother, but that's presumably conventional

Maximus

and GF(2)[x] is polynomials with coefficients from Z_2 correct?

Krijn

Yeah

I guess it's so that when you reach GF(4) you won't mistake it for $Z_4$

Semiclassical

8:17 PM

makes sense, yeah

the identification works for primes, but not for prime powers

Maximus

yeah, like Z_9 is not isomorphic to GF(9) since it's not even a field

correct?

Semiclassical

Z/9 is not a field, no

Krijn

Yeah

Maximus

Thanks guys!

Semiclassical

GF(9) is a field, but it's by necessity a different beast than Z/9

Maximus

8:18 PM

It's much clearer now, it was so confusing

Krijn

Field theory still confuses me sometimes

Often*

Daminark

@MatheinBoulomenos that is amazing. I'm just getting ready for classes on Monday

Semiclassical

Usually*

Daminark

@Maximus Z_9 = Z_3 x Z_3

Semiclassical

Though it's also confusing as a physicist since the physics meaning of 'field' is vastly different than the 'abstract algebra' meaning

Daminark

8:20 PM

Mathein knows I'm being cheeky here

Maximus

haha

Krijn

I was typing a very angry remark there...

Daminark

That's assuming I'm not horribly mistaken which isn't outside the realm of possibilites since my p-adic knowledge is limited

mercio

:s

Semiclassical

Which means that CFT means something very different to a mathematician than a physicist, (equally esoteric for both tho) despite them both being 'field theory'

mercio

8:21 PM

class(ical) field theories ?

Krijn

@Semiclassical Is CFT as beautiful for the physicist as it is for the mathematician?

Semiclassical

Conformal field theory

Daminark

Chromatic?

Oh

mercio

oh :(

Semiclassical

Conformal field theory

A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional algebra of local conformal transformations, and conformal field theories can sometimes be exactly solved or classified. Conformal field theory has important applications to condensed matter physics, statistical mechanics, quantum statistical mechanics, and string theory. Statistical and condensed matter systems are indeed often conformally invariant at their thermodynamic or quantum critical points. == Scale invariance vs. conformal... ==

Krijn

8:22 PM

:46929701

mercio

I need to learn that

Semiclassical

Where conformal is in the sense of complex analysis, i.e. preserving angles

Krijn

You were right for mathematics

MatheinBoulomenos

@Daminark $\Bbb Z_9$, if you define it as $\Bbb \varprojlim \Bbb Z/9^n\Bbb Z$, is just the same as $\Bbb Z_3$

Daminark

I was thinking just the power series interpretation

Semiclassical

8:23 PM

the following isn't quite right, but one gloss is that a CFT is a quantum field theory which is scale-invariant

Daminark

Since my category theory power level is limited

MatheinBoulomenos

hmm, I'm not sure. I don't usually think about p-adics where p isn't prime

Semiclassical

in more grounded physics, that usually shows up when you talk about a system in the vicinity of a phase transition

since there the relevant length scale that you use to describe the transition diverges

Daminark

This was mostly based on Wikipedia saying that the 10-adics are the 5-adics times the 2-adics tbh

Speaking of CFT: I've started going back through some parts of Neukirch, I'm now at the part that I skipped the first time on discriminants, and I feel I'm finding it easier to follow him

Semiclassical

as such, people like to describe the behavior of a system at the critical point in terms of CFT stuff

which is on the one hand great, because you get exact results and universal behavior

Krijn

8:25 PM

@Daminark Neukirch is great stuff :D

Semiclassical

but on the other hand it's horrible, because CFT is obscure

MatheinBoulomenos

@Daminark nice! ANT is still my favorite subfield of math

Krijn

Since when do we have ANT-fans in this chat

I've been away too long

Daminark

It's looking fun. I liked Milne but somehow he made the commutative algebra input really boring

Neukirch I guess is a bit more brisk and I sorta know what's aiming toward Dedekind domains

Krijn

I had a great class with just one other student and a very enthusiastic prof on CFT

He wrote his own book

You could try that

MatheinBoulomenos

8:29 PM

yeah, I really like Neukirch's style

Daminark

But when Milne just talked raw commalg I was like zzz

Lol luckily my professor agreed to do a reading course in NT this fall, not sure yet what it's gonna be, will discuss with him soon

But maybe CFT

MatheinBoulomenos

if you do the algebraic proof of CFT, be prepared for some technical group cohomology stuff

Krijn

Lol, I remember he said "and now we have to take a look at the kernel of this (Artin) map"

And then we looked at that kernel for three weeks or so, what the hell

I thought it would be five minutes

Semiclassical

For true crank material I want to see someone claim that CFT=CFT

Krijn

Let's see what the langlands programme can come up with

Semiclassical

8:35 PM

Oh, lol: mathoverflow.net/questions/74272/…

Maximus

to show that a polynomial is irreducible let's say in Z_3 it is sufficient to plug in all the elements of Z_3 and to show that they are not roots correct?

Krijn

@Semiclassical What the hell, I was jokin

Daminark

"Automorphic forms prove JFK assassination was by the CIA"

Semiclassical

I think that comment was intended as humor

Daminark

@Maximus that's if you're of degree ≤ 3

Krijn

8:37 PM

@Maximus I'm a bit out of this stuff, but couldn't it be two degree two polynomials multiplied

Semiclassical

This, on the other hand, appears to be serious if avowedly speculative: its.caltech.edu/~matilde/CFTtoCFT.pdf @Krijn

Maximus

Right, that makes sense

Is there a way to find such polynomials?

Daminark

@MatheinBoulomenos I've been meaning to learn group cohomology for sure, was probably the thing I would've done over the summer if not for complex multiplication

Krijn

@Semiclassical The article from Frenkel you mean?

Semiclassical

Oh, no

Daminark

8:39 PM

Also I ended up titling the paper "Elliptic Curves and Dreams of Youth"

Jasper Loy

@Semiclassical Do you know of any theoretical physics book series that goes all the way from classical mechanics to general relativity?

MatheinBoulomenos

@Daminark awesome

Semiclassical

I meant the KConrad comment

Krijn

Group cohomology has fun stuff, go for it!

MatheinBoulomenos

I assume you're referencing Kronecker's Jugendtraum

Semiclassical

8:40 PM

@JasperLoy landau lifshitz is the usual reference

Krijn

Or do Tate Cohomology at least

Daminark

@MatheinBoulomenos yeah I was

Jasper Loy

@Semiclassical I see. Is general relativity even covered there? I can't remember...

Krijn

@Semiclassical Yes but Langlands = Class Field Theory On Steroids

So your CFT = CFT was not too far off

Semiclassical

Good question, I dunno

I’ve never learned GR myself so I don’t know the relevant texts

Jasper Loy

8:41 PM

Well, I do know there is Theoretical Physics 1--8 by Nolting, but that doesn't touch GR.

I hope Milne publishes more of his notes into books in future.

Semiclassical

@Krijn huh

Guess it’s not quite as cranky as I’d have imagined

Daminark

Yeah Milne is quality. Actually I realized after I did my paper that some of the stuff about projective curves having points at infinity which babby Silverman didn't really explain well and which threw me off was way better explained in Milne's book on elliptic curves

Jasper Loy

Yeah, he has notes on AG and ANT.

In case you did not know, Anthony Knapp has Basic Algebra, Advanced Algebra, Basic Real Analysis, and Advanced Real Analysis on his website for free legal downloading.

And his Advanced Algebra does cover some AG and ANT.

The four books are very beautifully typeset and the diagrams are very beautiful. =)

Krijn

I wish I still did mathematics

Jasper Loy

You don't anymore @Krijn?

Krijn

8:50 PM

I'm in consultancy

MatheinBoulomenos

@JasperLoy I do like the table of contents of advanced algebra

Jasper Loy

@Krijn Better than me. I am a jobless lunatic.

Krijn

I do really cool stuff, and I couldn't go back to mathematics I think, but I do miss it sometimes

Jasper Loy

You know, you can always read math on your own, as a hobby.

Krijn

@JasperLoy I don't know if that's better; I'm a lunatic with money, which is far more dangerous

Daminark

8:51 PM

at least the money is good

Jasper Loy

@Krijn At least you have money. I don't.

Daminark

Actually question, did you have any specific experience that helped you get in to that? I'm kinda wondering how well one can just pivot into these kinds of jobs

Jasper Loy

@MatheinBoulomenos The four books together add up to over 2000 pages, lol.

Daminark

Versus do I actually have to learn to code

Jasper Loy

@Daminark I think consultancy is a very broad term.

Krijn

8:53 PM

Strategic consultancy basically looks for high-achievers, smart guys

Most mathematics graduates I know fit that profile

But then, there's a business aspect that most mathematicians don't feel comfortable with

I.e. I wear a suit every day