Mathematics - 2017-10-11 (page 1 of 7)

MatheiBoulomenos

00:00

okay then

Leaky Nun

:)

Faust

If i have an example i am usually not that dense

Ted Shifrin

@Faust: You definitely need to learn to take better notes and study them. Take the time to rewrite them. If you're going to borrow a friend's notes, don't just xerox them; copy them neatly and learn from writing.

Leaky Nun

how old is the verb "to xerox"?

Ted Shifrin

Your professor isn't using a textbook, Faust?

Leaky Nun

00:00

@MatheiBoulomenos I'm a constructivist

MatheiBoulomenos

@LeakyNun how do you finish the proof

Ted Shifrin

About 40 years, Leaky.

Leaky Nun

[I know, formal rational function is still constructive]

MatheiBoulomenos

I'm a non-contructivist. I always prefer the non-contructive proofs

Leaky Nun

@MatheiBoulomenos well, just take the subgroup of $S_n$ that is isomorphic to your desired group

Daminark

00:01

@MatheiBoulomenos same

Leaky Nun

@Daminark kicks Demonark

Faust

@TedShifrin my prof is using a buncha of notes cut from a book where he does exercises out of his notes (available by pdf) usually there i at least one worked out example for each idea and the rest are exercises which we usually cover in class

Daminark

moves foot out of the way

MatheiBoulomenos

okay, yeah I think you got it

Leaky Nun

@MatheiBoulomenos that's nice

Ted Shifrin

00:02

OK, Faust. I think it would help you to look at a book that's similar to what he's doing. Ask him for a resource.

MatheiBoulomenos

Nice job coming up with using Cayley's theorem! That took my a while when I solved that exercise

Leaky Nun

@MatheiBoulomenos lol thanks

Daminark

I can't remember if I've said this on here or whether it was somewhere else, but always use the axiom of choice when possible. Even if you're only doing finite sets

Leaky Nun

adjoining n elements would have took me forever

Ted Shifrin

taken, Leaky, not took

Daminark

00:03

"tooken"

Leaky Nun

Sep 11 at 19:08, by Daminark

If you have an opportunity to invoke choice, do it

@TedShifrin was that really necessary?

Ted Shifrin

gives Demonark a token of my ... lack of esteem

Faust

@TedShifrin since i have an ideaic memory i just memorize the entirety of his notes and all examples and work out all exercises for myself. it only takes 2 or 3 passes to memorize every definition and example and solution to every exercise. the problem is if i have no example and cant remember what we did i cant solve any of the exercises

Leaky Nun

maths isn't a memorization test.

Daminark

Okay so it was here then, nice

Ted Shifrin

00:04

You asked me to correct your German, Leaky, so I assumed you wanted me to correct your English.

Leaky Nun

@Daminark I've quoted it like three times

@TedShifrin oh, lol alright

sorry :P you may continue correcting

Ted Shifrin

I don't do it often, but the Brits are much more up tight about proper syntax.

MatheiBoulomenos

I will gladly correct anyone's German, if anyone wants me to

Faust

@LeakyNun the only part of math i find difficult consistently is understanding what is written after that math is usually quite trivial

Leaky Nun

@MatheiBoulomenos ich will

Ted Shifrin

00:05

Teehee.

MatheiBoulomenos

Please correct my English as well

Leaky Nun

@MatheiBoulomenos klar

Faust

@LeakyNun memorizing every definition helps with understanding significantly

Daminark

@Leaky 'tis true, though I tend not to keep too many tabs on my interactions, and most of my shitposting is IRL anyway, so I never remember how much bleeds

MatheiBoulomenos

@LeakyNun "ich will" is grammatically correct, but if you say that, people will associate it with marriage :P

Leaky Nun

00:07

@Daminark you see, after all it's the axiom of choice

@MatheiBoulomenos oh danke

wie sollte ich es sagen?

MatheiBoulomenos

Hmm, du kannst sagen z.B. "Bei mir gerne!"

Leaky Nun

lol ok

Balarka Sen

Hm, I woke up.

Leaky Nun

hi

Ted Shifrin

Go back to sleep, Balarka.

3

MatheiBoulomenos

00:08

Solange du noch irgendwas anderes im Satz hast außer die zwei Worte "ich will", denken die Leute auch nicht an Hochzeit.

Daminark

@BalarkaSen Not sure I buy that, you seem asleep

Leaky Nun

@TedShifrin LOL

Ted Shifrin

Leaky ist aber ganz jung ...

Balarka Sen

@TedShifrin Easier said than done!

MatheiBoulomenos

Also "Ich will, dass du mein Deutsch korrigierst" wäre auch okay, aber vielleicht ein bisschen lang

Hi @BalarkaSen

Balarka Sen

00:09

u should write a book, "Sleeping: A Geometric Approach"

6

Ted Shifrin

Es gibt kein ß mehr :(

Balarka Sen

Hi @MatheiBoulomenos

Ted Shifrin

@Balarka: My students would say easy ... just listen to a Shifrin lecture.

Balarka Sen

ahaha

MatheiBoulomenos

Es gibt schon noch ein ß, aber dass weißt du bestimmt @TedShifrin

Ted Shifrin

00:10

warum dass?

Balarka Sen

so what happened in the brief period i was asleep?

Ted Shifrin

Mostly agony.

Daminark

@Ted The lectures of yours that I've seen online seemed to be more dynamic than others

Ted Shifrin

I made Faust suffer for an hour and he made me suffer an hour.

Daminark

And they weren't even on dynamics shrug

Balarka Sen

00:11

mutual suffering, mmm

that's what i live for

Ted Shifrin

oh, and Mathei told Leaky that he, Leaky, wants to get married.

Balarka Sen

Congrats

Ted Shifrin

Demonark: If you go to the end, there are a few on systems of ODE.

MatheiBoulomenos

by the way, it is possible to conclude that $\mathbb{Z}^3/N \cong \mathbb{Z}^2$ without showing that $\phi$ is surjective

Ted Shifrin

Doing normal form for the matrix?

Sure.

Balarka Sen

00:12

I hope he invites us in his marriage anniversary

Daminark

Ah, nifty

Ted Shifrin

I didn't want to teach Faust how to do $\Bbb Z$ row and column operations.

Balarka Sen

@Daminark thinks ODEs are not cool

Daminark

I mean I didn't like my (admittedly brief) shtick with ODEs as much as I've liked other things but I don't have much of a reservation against them

Ted Shifrin

Demonark only likes formal mathematics.

And that doesn't include forms.

Eric Silva

00:15

@Daminark is a reprobate so idk if his opinion should be held in high esteem

Daminark

Actually I've got a soft spot for forms, they're pretty nice

Ted Shifrin

I don't, @EricSilva.

Daminark

But yeah it's really just that I had a lot of other things I'm gonna be doing so ODE just isn't high on my priority list

MatheiBoulomenos

I was thinking about something like this: tensor the exact sequence $0 \to N \to \mathbb{Z}^3 \to \operatorname{Im}(\phi) \to 0$ with $\mathbb{Q}$, using that $\mathbb{Q}$ is flat over $\mathbb{Z}$, apply rank-nullity to the tensored sequence to conclude that the rank of $\operatorname{Im}(\phi)$ is $2$

Then use the fact that submodules of a finitely generated free module over a PID are again free and finitely generated, to conclude that $\operatorname{Im}(\phi)$ must be a free $\mathbb{Z}$-module of rank $2$

Daminark

@Eric It's not really an opinion so much as taste

Eric Silva

00:16

was being overtly facetious

MatheiBoulomenos

This way, you only need to show that $N \otimes \mathbb{Q}$ is 2-dimensional

Balarka Sen

Daminark is an algebraic hippie

Ted Shifrin

Right, @Mathei: I was thinking about the cokernel when you do generators and relations.

Obviously, @Mathei, that was the desired solution.

MatheiBoulomenos

That way, you only need to do row operations over $\mathbb Q$

Obviously

Ted Shifrin

I like doing row and column operations over $\Bbb Z$ or $F[x]$. Not so much a general PID.

Leaky Nun

00:18

The answer to the question "is $\Bbb Q(\sqrt2)$ isomorphic to $\Bbb Q(\sqrt3)$" is both "yes" and "no"

Ted Shifrin

A question is neither "yes" nor "no".

MatheiBoulomenos

well, of course it is

Daminark

Lol, I still haven't gotten good at figuring out, "facetiousness" (watch me get rinsed if that's not the right word) over the internet

Leaky Nun

@TedShifrin edited

Ted Shifrin

So I see :)

So isomorphic in which category ... is the question.

MatheiBoulomenos

00:19

if you don't specify the category, then everything is isomorphic to everything else and not isomorphic to everything else

Leaky Nun

hmm

Daminark

@TedShifrin Peter May intensifies

Ted Shifrin

Oh, you're gonna get Leaky started on $\Bbb R\cong \Bbb R^2$.

MatheiBoulomenos

they are isomorphic as Abelian groups!

Balarka Sen

field extensions are p dumb as vector spaces

MatheiBoulomenos

00:19

but not for a constructivist :P

Ted Shifrin

I liked this room when we did geometry and analysis.

Leaky Nun

I am not a constructivist

Eric Silva

@Daminark i used the word reprobate, i would never use such a word seriously lmao

Ted Shifrin

Eric, I will reproach you if you don't.

Leaky Nun

@TedShifrin you got yourself started on that

MatheiBoulomenos

00:20

Galois theory is a special case of the theory of étale fundamental groups and thus geometry @TedShifrin

Balarka Sen

@MatheiBoulomenos Nah.

Eric Silva

pls

MatheiBoulomenos

@TedShifrin but algebraic geometry is geometry

Ted Shifrin

I'm not saying anything.

Daminark

Make sure the title of your thesis includes "A Geometric Approach" and you're good @Eric :P

Balarka Sen

00:22

Depends on the percentage of algebra and geometry in algebraic geometry

Ted Shifrin

I knew I would be ridiculed for decades when I subtitled the second book tongue in cheek.

Daminark

(@Ted sorry if repeated usage is getting annoying, but it's just great)

Balarka Sen

I love Geometric Approaches

Ted Shifrin

@Mathei: I did algebraic geometry (at least, what I did) over $\Bbb C$.

MatheiBoulomenos

:O

Eric Silva

00:23

$\Bbb C$ or bust tbh

Balarka Sen

$\Bbb C$ is the only algebraically closed field ever so that's redundant to mention, @Ted

Daminark

Only algebraically what?

Ted Shifrin

I guess $\bar{\Bbb Q}$ is a pigment of the algebraists' imagination.

Leaky Nun

@TedShifrin btw I can't find any of your books in the Imperial library

Eric Silva

@Daminark geometric geometry: a geometric approach

Leaky Nun

00:24

should I burn it down?

Ted Shifrin

No, Leaky, it just shows that they have impeccable taste.

Daminark

Algebraic closure of $\mathbb{Z}/91\mathbb{Z}$ ftw

Balarka Sen

@Daminark Closed.

Daminark

(Psyche, 91 is actually the most troll number)

Leaky Nun

@TedShifrin why is it impeccable?

@Daminark what's special about it?

that is isn't even a field?

Eric Silva

00:25

@Daminark cause it's not prime?

Daminark

Nope, 91 isn't prime

Balarka Sen

yeah, we all know that joke by now

Daminark

Which is seriously annoying because it's supposed to be prime

MatheiBoulomenos

I mean $\mathbb C$ is just any algebraically closed field of characteristic $0$, why are you so obsessed with that one

Balarka Sen

pls no dead memes

Daminark

00:26

But yeah I mean I dunno, are algebraically closed fields of characteristic p not a thing people think about? It's gotta come up somewhere

MatheiBoulomenos

I prefer to contruct it as the completion of the algebraic closure of the $p$-adics :P

Balarka Sen

@MatheiBoulomenos Characteristic? Huh? Never heard of that

@Daminark It is, we are all joking

Ted Shifrin

Me? @Mathei — because I am a complex differential geometer.

Balarka Sen

characteristic p algebraic geometry is where all the number theory are

2

Ted Shifrin

<--- never cared for number theory

Daminark

00:27

Oh... meh I need to stop taking things seriously

MatheiBoulomenos

I mean as a fields $\mathbb{C} \cong \mathbb{C}_p$

Balarka Sen

@Daminark lmao y so serious

Leaky Nun

@MatheiBoulomenos what the hell

Balarka Sen

completion of closure of p-adics

Daminark

If I just embrace my shitposting potential I will never be bamboozled

Balarka Sen

00:28

we are doing a bamboozle switcharoonie on you

Eric Silva

@Balarka wut abt characteristic p differential geometry

Leaky Nun

complex conjugate should be called real-conjugate

but it's too late to change the name now

[I just read it today but I forgot where I read it]

Daminark

$\text{Char}^p$ spaces emirite?

Ted Shifrin

Hi DogAteMy

Akiva Weinberger

Hi

Leaky Nun

00:29

math.uconn.edu/~kconrad/blurbs/galoistheory/galoiscorr.pdf

Balarka Sen

@EricSilva u should do p-adic differential geometry

Leaky Nun

2.3 here

Eric Silva

it's all abt PDEs in char p my d00d

Balarka Sen

p-adic analytic manifolds are a thing

MatheiBoulomenos

I mean, you can define $D$-modules in characteristic $p$

Balarka Sen

00:30

so theres that

Daminark

Oh that sounds sick

Eric Silva

@Daminark @Balarka math.unm.edu/~buium/adgintro.pdf

Daminark

:40475542 "Algebraic Number Theory: A Geometric Approach"

Akiva Weinberger

One Yale question was "If you could teach a course what would it be called" (not the exact quote)

Ted Shifrin

The Higher Arts of Punnery

Balarka Sen

00:31

"A Course in Yale"

Ted Shifrin

as in ... Get Thee (all) to a Punnery (except for Demonark, who needs to go to a Nunnery)

Eric Silva

"keep out"

Daminark

I should drop math and major in puns tbh, that's got a future

mdave16

I just got de ja vu, i could have sworn i'd read this just moments ago

Akiva Weinberger

I wrote "Nonstandard Analysis: Hypperreals and Internal Set Theory"

Daminark

00:31

Noice

Ted Shifrin

DogAteMy: Nobody in Admissions knows math.

Balarka Sen

I would not take that course

MatheiBoulomenos

"Algebra and nothing but Algebra"

Eric Silva

I would stay the hell away from that tbh

Akiva Weinberger

'cause it's a real thing and I feel like I could probably do it with enough time to prepare

@TedShifrin Yeah, all they need to know is that it looks math-y

Balarka Sen

00:32

@EricSilva We're bros

Ted Shifrin

They want you to teach a course of interest to someone other than you.

Meh.

Akiva Weinberger

@EricSilva @BalarkaSen Shut up nonstandard analysis is amazing

:P

Eric Silva

i would take a course just called "interesting things"

Balarka Sen

@Akiva to normies, perhaps

MatheiBoulomenos

If I taught a course called "interesting things", it would be algebra and number theory

Akiva Weinberger

00:33

@EricSilva Just a collection of mildly interesting gifs

Eric Silva

or a course on just fun facts

that'd be fun

Leaky Nun

@MatheiBoulomenos and everything about the empty set

(what is the field generated by the empty set?)

Akiva Weinberger

@EricSilva Well clearly or else it's false advertising

MatheiBoulomenos

"the empty graph - a pointless concept?"

Leaky Nun

@MatheiBoulomenos right

Daminark

00:35

Oh that was good @Mathei

Balarka Sen

@MatheiBoulomenos I remember once I was in a topologists's office when he wasn't there, and he came rushing in, banging the office doors shut and hurling insults to thin air. It turned out he was in a conference and it was about algebraic D-modules.

Leaky Nun

@AkivaWeinberger no first-order axiomatization of the reals can disprove the existence of infinitesimal

Akiva Weinberger

@Daminark I think that's an actual paper

Eric Silva

@Akiva ooh how about a course called "false advertising"

Leaky Nun

(compactness theorem) @AkivaWeinberger

Akiva Weinberger

00:35

@LeakyNun Yup

Daminark

Oh snap @Leaky

MatheiBoulomenos

Yes, I stole that one from a paper

Leaky Nun

@AkivaWeinberger you know compactness theorem :O

Akiva Weinberger

I mean, assuming you're defining "infinitesimal" the right way

Leaky Nun

how do you know lol

mdave16

00:36

was the question, what is title of course, if you were teaching?

Akiva Weinberger

@LeakyNun Only from like Wikipedia and occasionally talking to Noah Schweber (guy from Mathcamp)

Leaky Nun

@AkivaWeinberger oh cool

Akiva Weinberger

@mdave16 Yeah

Leaky Nun

me too, user21820 instead of Noah Schweber

Balarka Sen

Other people can read wikipedia too, yes. Fascinating, isn't it

7

Leaky Nun

00:36

@BalarkaSen yes

go away /s

mdave16

i would teach a course called "very easy module" and put in all the hardest things i knew, not even related, just all the hardest things

Akiva Weinberger

"Like planking, that's hard"

Daminark

@mdave16 is it a vector space tho?

Eric Silva

ur a vector space @Daminark

mdave16

it's a point set, you could put a topology on it, but not much else

MatheiBoulomenos

00:38

@BalarkaSen I don't know, the idea of using algebra to prove things about PDEs seems like a fascinating idea to me. Just to show those analysts that algebra is useful

Balarka Sen

he's a vector space over F_1

the field with one element

Leaky Nun

so tensor is basically a generalization of ever linear algebra concept I've ever learnt?

mdave16

i keep being asked this at interviews for real-world jobs

Leaky Nun

I should borrow a book on tensor after I finish reading Galois theory

Akiva Weinberger

insert English-French pun here

mdave16

00:38

"why is algebra useful/helpful to this company"

Balarka Sen

@LeakyNun no it's just multilinear algebra

Daminark

@Eric no u

Ted Shifrin

@AkivaWeinberger huh?

Leaky Nun

@BalarkaSen I mean, it includes scalar and vector and linear transformation and cross product

Akiva Weinberger

@TedShifrin F_1

is Fun

Balarka Sen

00:39

F_un

Ted Shifrin

ohh :(

MatheiBoulomenos

@mdave16 and I thought for a moment that you're being asked if you're a vector space :D

Ted Shifrin

I wasn't paying detention to the drivel.

mdave16

these interviews be cray, i keep disappointing by not being a vs

Balarka Sen

@MatheiBoulomenos Haha. Well, I definitely know bits of algebra which are actually useful in real life

Akiva Weinberger

00:40

I've heard that, algebraically, differentiation is easy and integration is hard, while numerically, integration is easy and differentiation is hard

MatheiBoulomenos

Who cares about numerics

Leaky Nun

@AkivaWeinberger hice una prueba sobre espanol y soy level 3 lol

Akiva Weinberger

(Semirandom (re: differentiation etc))

Eric Silva

@MatheiBoulomenos more ppl than care about pure math tbh

Ted Shifrin

^^yup

Leaky Nun

00:41

@AkivaWeinberger that's... nice

Akiva Weinberger

@LeakyNun Is "prueba" test or proof I forget

Leaky Nun

test

Akiva Weinberger

You made a test…?

Daminark

@mdave16 I'm still holding out that I can get a job in compsci by getting good at number theory or something

Leaky Nun

@AkivaWeinberger I did a test

CausingUnderflowsEverywhere

00:41

@LeakyNun Explicit is very important in precise science such as mathematics.

Leaky Nun

how would you say that? @AkivaWeinberger

Eric Silva

idk many analysts who don't also kind of like algebra, there are just vast swaths of algebra that aren't useful to them @Mathei

Akiva Weinberger

Oh… tomaste una examen

mdave16

@Daminark, i was doing this, i did not think it through

Leaky Nun

@AkivaWeinberger oh, right

tome una examen de espanol

well it's really an entrance test

MatheiBoulomenos

00:42

@EricSilva I'm not really being serious

Akiva Weinberger

Is "level 3" the score you got?

Daminark

What do you mean @mdave16?

Akiva Weinberger

(Level = nivel)

Faust

Did he just ping himself?

mdave16

@Daminark, and i did computational algebraic number theory, i did lots on algos and programming, still nobody hires me :'(

Leaky Nun

00:43

(pero lo he puesto a mi 3a preferencia lol)

@AkivaWeinberger yes

3rd level of proficience

Akiva Weinberger

3 out of…?

Leaky Nun

hay como 6 niveles

Akiva Weinberger

Ah

Well congrats

Leaky Nun

Common European Framework of Reference for Languages

The Common European Framework of Reference for Languages: Learning, Teaching, Assessment, abbreviated in English as CEFR or CEF or CEFRL (compared to the German abbreviations GeR or GeRS, the French abbreviation CECR, the Italian QCER, or the Spanish MCER), is a guideline used to describe achievements of learners of foreign languages across Europe and, increasingly, in other countries. It was put together by the Council of Europe as the main part of the project "Language Learning for European Citizenship" between 1989 and 1996. Its main aim is to provide a method of learning, teaching and assessing...

Daminark

Shit...

mdave16

00:43

@Daminark, shit indeed

Daminark

Yeah I should just permanently move into the Barn after graduating

Balarka Sen

i wish i didn't have to study and have a career in math

Eric Silva

@Daminark you should do what Chris did, leave for grad school, come back to uchicago as a postdoc, then get constantly roasted by ur former profs

Ted Shifrin

you don't have to, Balarka

you can be a business bum

Eric Silva

for getting a crappy uchicago education

mdave16

00:45

i'm now applying for phds again, on the plus side, you will get several interviews Dam, i get at least 2 a week without applying, and goes up to about 9 if you do

Leaky Nun

How hard is it for me to learn Markov chains?

@TedShifrin

Daminark

@Eric Chris?

Eric Silva

one of the dickson intructors

Daminark

I see

Lmao

Eric Silva

he's a pde man

Ted Shifrin

00:46

I don't know what you mean .. it's basic probability/linear algebra.

Eric Silva

luis makes fun of him for not having learned linear algebra

Ted Shifrin

No comment @EricSilva.

Balarka Sen

lmao

Daminark

Well... doing that requires actually coming here as a postdoc... but yeah good life goal

Also LOL

Ted Shifrin

Not to mention multivariable calculus. no comment

Akiva Weinberger

00:46

"On a scale from one to ten, how confident are you that today's date is 10 in binary" "10/10"

Eric Silva

no comment intensifies

MatheiBoulomenos

I personally never learned ODEs and I'm not planning to

Daminark

@Mathei I probably should do it but I've got way too much going on

Balarka Sen

beautiful swirly phase diagrams

mdave16

how do you never learn ODEs?

MatheiBoulomenos

00:48

It's not required at my school

Akiva Weinberger

They're so ordinary

and differential and equation

mdave16

if you know how to differentiate, you already know ODEs

Daminark

@AkivaWeinberger In contrast to freakish differential equations

Ted Shifrin

rolls 10 eyes at pompous attitudes

Eric Silva

@Daminark that's my niche

Akiva Weinberger

00:49

I've basically forgotten ODEs anyway

I'm probably not gonna learn PDEs ever tbh

Balarka Sen

@TedShifrin It feels like I've grown up a lot, don't you think?

Akiva Weinberger

I mean maybe but I don't plan on it

Ted Shifrin

Yup, @Balarka.

MatheiBoulomenos

the thing is I want to do algebra and number theory, I don't think ODEs are going to be helpful for that

Eric Silva

@Akiva they're pretty cool tho

Ted Shifrin

00:50

They're actually very beautiful, DogAteMy, especially re geometry.

Akiva Weinberger

I know nothing about them

Hm, maybe I should look them up a little

Balarka Sen

@Akiva we're supposed to learn covering spaces

Daminark

@Akiva it's like you take a differential equation and split it in half, and each one is a partial differential equation

MatheiBoulomenos

I know how to prove Picard-Lindelöf, that should suffice

Akiva Weinberger

I like how Daminark teaches things, he should teach more things

Daminark

00:51

Truly

Leaky Nun

@TedShifrin is this a response to me?

Daminark

Anyway that's enough trolling for today, I need to get to work

Balarka Sen

he's too busy t h o n k i n g

Eric Silva

@Daminark how do u get a stochastic de

Akiva Weinberger

@LeakyNun Markoviness I think

Daminark

00:51

@EricSilva Use Stoche's'' theorem on a PDE or something?

Leaky Nun

@AkivaWeinberger ??

Daminark

But yeah see you guys around!

Akiva Weinberger

6 mins ago, by Leaky Nun

How hard is it for me to learn Markov chains?

Balarka Sen

It seems the chat has actively partitioned itself between algebra-inclined people and geometry-inclined people

MatheiBoulomenos

Have fun trolling elsewhere @Daminark

Balarka Sen

00:52

@Mathei loooool

Leaky Nun

@AkivaWeinberger was that a serious response?

'stoy 'nserio

Akiva Weinberger

What I meant was, "it probably was a response to you"

Leaky Nun

lol

well I've never come across it before

Eric Silva

@Balarka the thing is tho, i still like algebra, i just like literally every other part of math that isn't logic or set theory better

Leaky Nun

but if the prerequisite is just basic probability and linear algebra then I think I perhaps can manage it

mdave16

00:54

@BalarkaSen, but where do the algebraic geometers go?

Akiva Weinberger

I don't know how it works, but at a guess you keep a vector full of probabilities of the possible outcomes… or something

Leaky Nun

@EricSilva logic and set theory are my favourite :'(

Eric Silva

and that's great, i just do not enjoy them, and not for want of trying

Balarka Sen

@EricSilva I honestly do not dislike algebra

Ted Shifrin

I think there's an example in the applications section of Chapter 9 of my book, DogAteMy.

Akiva Weinberger

00:54

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Balarka Sen

My primary filtering device is topology. I see everything with a pictorial point of view

Leaky Nun

@TedShifrin if only I could borrow them

MatheiBoulomenos

If I could do bachelor in algebra instead of math, I would do it

Leaky Nun

@BalarkaSen how do you represent $\Bbb Q(\sqrt2)$ with a picture

Ted Shifrin

Leaky, I am told you can find most books illegally on the internet.

Balarka Sen

00:55

@LeakyNun two-fold cover

Leaky Nun

@MatheiBoulomenos bachelor in galois theory :P

MatheiBoulomenos

sounds fun

Leaky Nun

@TedShifrin :c

mdave16

@TedShifrin, such is correct

Akiva Weinberger

$\fbox{$\Bbb Q(\sqrt2)$}$

Leaky Nun

00:55

@BalarkaSen $\Bbb Q_p$?

Akiva Weinberger

^Picture of $\Bbb Q(\sqrt2)$

Ted Shifrin

I believe 3 of my 4 books can be found (including the 1 I have publicly in .pdf form).

Balarka Sen

p-adics are the most geometric thing algebra has to offer

Eric Silva

@Balarka i think ive gotta a pretty even split between thinking pictorially and thinking in terms of equation shenanigans

Balarka Sen

p-adic solenoids

Akiva Weinberger

00:56

@BalarkaSen Hrm?

Leaky Nun

@BalarkaSen $\overline{\Bbb Q}$?

Balarka Sen

universal cover

Leaky Nun

$\Bbb Z_7(i)$?

Balarka Sen

two fold cover of the circle

MatheiBoulomenos

@BalarkaSen how do you imagine the property of being faithfully flat

Balarka Sen

00:57

@EricSilva Yeah, as an analyst should have!

Leaky Nun

@MatheiBoulomenos a muslim praying on the floor

Akiva Weinberger

Balarka are you just making stuff up

Eric Silva

i do so many long calcs

Leaky Nun

@TedShifrin welche buch?

Balarka Sen

@Akiva Nope, I am just using the covering space - Galois extension dictionary.

MatheiBoulomenos

00:58

*welches Buch

Leaky Nun

I heard Galois

@MatheiBoulomenos thanks

Ted Shifrin

Leaky: The one with the most on Markov is the linear algebra book with Adams. We even proved a convergence theorem in there.

Leaky Nun

cool

Balarka Sen

@MatheiBoulomenos Hm, I am pretty sure I had a picture for this when I knew this stuff. Flat modules are exact sequence preserving after tensor, right?

MatheiBoulomenos

Right.

Faithfully flat modules reflect and preserve exactness

Leaky Nun

00:59

I'll leave my description blank.

Ted Shifrin

Right. Now write down the transition matrix.

Leaky Nun

too much time on the internet

Balarka Sen

@MatheiBoulomenos So R-modules are actually like vector bundles w/ varying fibers over Spec R

Leaky Nun

@TedShifrin lol, you spent too little time on the internet

Balarka Sen

I think there's a precise description for certain types of modules

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$Mathematics$ Mathematics