Mathematics - 2018-02-18 (page 5 of 7)

Akiva Weinberger

17:00

He just computes some homology groups of some simplicial complexes

0celo7

@XanderHenderson I use Mac, Windows, and Linux.

I agree, Preview is good for Mac

Xander Henderson

For Mac, I like Skim

Akiva Weinberger

$\rm Alg^\top$

bolbteppa

The only bad thing about adobe I've found is not being able to edit pdfs to make your own bookmarks when lecturers make notes without bookmarks (which I think is in the full version)

0celo7

@bolbteppa I wonder if I can get the full version from my school

bolbteppa

17:01

and the update thing

0celo7

It would be pretty sweet

bolbteppa

Yeah, mathematica is usually free too

0celo7

I can't use it until I restart...which I won't do for a while

Dammit

Hmm. I can open and use Adobe

But it keeps giving me an error

r/softwaregore

bolbteppa

Wild's history course is pretty good, the real numbers comments he comes out with are just ridiculous

0celo7

can anyone succinctly and accurately explain what Wildberger's issue with R is?

Daminark

17:03

Not even he can tbh

bolbteppa

Imagine denying that $\sqrt{2}$ exists while believing in Pythagoras' theorem

Eric Silva

njwildberger.com/2012/12/02/difficulties-with-real-numbers

Daminark

Jk I dunno, I get the vibe that he just doesn't trust numbers that can't be explicitly described

Mats Granvik

Programming formulas in Mathematica or any other software is so easy compared to writing them out in latex in a correct way. Latex does not compute anything. We need latex that would actually compute something that would tell you if your reasoning is correct or not.

Akiva Weinberger

@0celo7 Infinity is too many

I guess

0celo7

17:08

@AkivaWeinberger Does he have an issue with countable infinity?

Akiva Weinberger

Not sure; probably

Ted Shifrin

Hi DogAteMy!

Akiva Weinberger

Oh, well

0celo7

"However with the advent of relativity theory and quantum mechanics, the concept of the continuum again became murky" oh fuck off

Akiva Weinberger

He believes $\Bbb Q$ exists, I think

so maybe not

@TedShifrin Heyup

Eric Silva

17:09

he's the kind of dude who makes a kind of reasonable philosophical stance look bad

Daminark

So I dunno any physics and thus cannot comment, but why ought that influence a construction of thought?

Ted Shifrin

Luckily for me, I haven't experienced him and I don't intend to.

Akiva Weinberger

I was in a lecture on Kierkegaard yesterday, I was not enthused

Philisophy is not for me

Daminark

Whatever trying to reason through his stuff probably isn't the best idea

Eric Silva

@AkivaWeinberger kierkegaard is basically just lit

barely philosophy

bolbteppa

17:10

Seems like he's saying, you can't list the real numbers, ergo they don't exist

Ted Shifrin

My freshman year I took a couple of courses on philosophy of education. Quite interesting.

0celo7

@Daminark quantum mechanics implies certain energy levels are discrete, not that everything is discrete

Akiva Weinberger

@TedShifrin What, like pedagogy?

@bolbteppa Hell, you can't even describe most of them

That probably has to do with stuffs

Eric Silva

@TedShifrin education is a prison for our souls (a la Foucault)

Ted Shifrin

No, definitely not. This was 1970, so I've forgotten a lot, but we started with some of the Greek philosophers' writings on education/learning and worked up to modern.

mercio

17:12

a prison o..o

Akiva Weinberger

Hm

Abcd

I need tips to improve my maths speed and efficiency. I want to make myself capable of doing 30 hard questions in 1 hour. Please guide me.

Akiva Weinberger

I wonder what would happen if I were to look up "Learning" on Wikipedia

mercio

practice

bolbteppa

If you ever look at the YT comments on his videos, I'd say he's misleading a lot of people with this garbage and his "we need to understand mathematics in the right way before we will be able to unlock the deepest secrets of the universe" nonsense is not a joke

Eric Silva

17:12

o lol that's before the thing im referencing was written i guess

Akiva Weinberger

Learning

Learning is the process of acquiring new or modifying existing knowledge, behaviors, skills, values, or preferences. The ability to learn is possessed by humans, animals, and some machines, and there is also evidence for some kind of learning in some plants. Some learning is immediate, induced by a single event (e.g. being burned by a hot stove), but much skill and knowledge accumulates from repeated experiences. The changes induced by learning often last a lifetime, and it is hard to distinguish learned material that seems to be "lost" from that which cannot be retrieved. Human learning begins...

bolbteppa

"difficulties lead to weakness in the calculus curriculum", ah it's the subjects fault I can't do the integral, not my fault...

Abcd

@TedShifrin can you see my question please?

Eric Silva

im sure WILDberger can do integrals

Akiva Weinberger

Wrong name!

Eric Silva

17:14

lmao

my bad

Ted Shifrin

@Abcd: I agree with mercio. Practice is essential. And, as I've commented to you before, stop being stubborn about certain things if they slow you down :) But, for goodness sake, you worry too much and make it stressful rather than fun.

Mike Miller

I mean, I am sure you can do integrals

Eric Silva

^

Akiva Weinberger

Hi

Abcd

@TedShifrin I worry because they give very hard questions in my exam :(.

Akiva Weinberger

17:15

$\int f(x)=F(x)$

$\int\ln(x)={\rm LN}(x)$?

Pretty sure that's how it works

Abcd

Today I had my exam, I could do physics properly but no maths at all! Questions were reallly hard.

0celo7

@EricSilva Is it true that a Riemannian 3-torus has an embedded minimal 2-torus?

Ted Shifrin

But worrying doesn't help, Abcd. Just enjoy doing math and do the best you can do ... But definitely—if time is an issue—spend more time thinking about what's more efficient.

Abcd

Okay, and I'll also start being more receptive towards quick methods from now onwards.

Alex K Chen

Under which condition on rational $R, Q$, the quantity $[R + \sqrt{Q^3 + R^2}]^{\frac{1}{3}} + [R -\sqrt{Q^3 + R^2}]^{\frac{1}{3}}$ would turn out to be an integer ? (Basically I'm finding integer solutions to a cubic diophantine, and this is a crucial step)

Akiva Weinberger

17:22

Oh, I probably used to know stuff like this

Alex K Chen

OK then tell me the sketch, I'll fill up the details

Akiva Weinberger

I don't remember, though

Mike Miller

I feel like that was a really aggressive way to ask for help

Akiva Weinberger

I guess one possible approach is to cube it and hope stuff happens?

Hm, let me think up a concrete example

mercio

it's a rational if and only if the cube roots are in that quadratic extension

and it's an integer almost if and only if those cube roots are algebraic integers too

Akiva Weinberger

17:24

$(7+5\sqrt2)^{1/3}+(7-5\sqrt2)^{1/3}=2$

I think

Alex K Chen

yea

@mercio wtf

Balarka Sen

alerting the drama here

0celo7

@AkivaWeinberger how on earth

Alex K Chen

@0celo7 Roots of the cubic

0celo7

what?

Alex K Chen

17:25

lemme reverse engineer cardano

Akiva Weinberger

@0celo7 Because $(1+\sqrt2)^3=7+5\sqrt2$, and $(1-\sqrt2)^3=7-5\sqrt2$

0celo7

@BalarkaSen do you have questions about Evans, I'm trying to avoid dealing with my own PDEs

Alex K Chen

ok so what's the general method to find out if they forms an integer

Balarka Sen

write a = cbrt(7 + 5qrt(2)) and b = cbrt(7 - 5sqrt(2)), then (a + b)^3 = a^3 + b^3 + 3ab(a + b). write x = a + b, then x^3 = 14 - 3x

x = 2 is a root. do some fuckery to see that the other two can't be

3

Ted Shifrin

covers innocent ears

Balarka Sen

17:28

the other two has to be complex

mercio

pick a random (a+sqrt(b)) and decide that the cube of that guy is (r + sqrt(q^3+r^2)), and express q and r in terms of a and b

Alex K Chen

:o brilliant

Balarka Sen

@0celo7 I am running out of time to read any math whatsoever

Alex K Chen

this would suffice

@BalarkaSen aren't your boards from march 27 ?

0celo7

@BalarkaSen Same

All I do is math, but not the right math

mercio

17:29

i think i get q=b-a² and r=a^3+3ab

0celo7

feelsbadman

Balarka Sen

@Alex yes

Alex K Chen

good luck for chemistry

Joe Shmo

@TedShifrin, sometimes at the beginning of lecture you're talking about things you haven't gone over in class. is it a recitation you're referring to or a homework assignment?

Ted Shifrin

No recitations, @JoeShmo, but, yes, homework questions (either WeBWork — on line — or book questions).

Joe Shmo

17:32

ok. just making sure i haven't missed anything

Ted Shifrin

Well, have you turned in all your homework problems? :P

Balarka Sen

@AkivaWeinberger are you a young inspiring poet? do you have nothing but bilious hatred for the class enemies? do you suffer in your everyday life from identity crisis and meaninglessness? boy, do i have the genre for you

it's called E X I S T E N T I A L I S M

Akiva Weinberger

The answer to all homework problems is "Exercise for the reader"

MatheinBoulomenos

What am I supposed to do? I want to TA number theory, but I also want to TA intro complex

Akiva Weinberger

Hrm, "Exercise for the grader"

mercio

17:33

@AlexKChen cardan's formula are kinda useless to solve cubic equations in practice

0celo7

@AkivaWeinberger the grader should make sure he knows the material

Joe Shmo

well, so far i turned them all in, to a different guy :)

i'm learning from you, answering to somebody else.

Ted Shifrin

Hmm, well, I suppose that's just as well — I'm tired of grading.

Alex K Chen

@mercio It doesn't matter, because I'm only interested in integer solutions to the cubic $x^3 -2xy^2 + 2y^3-1 = 0$, and for this cardano (w.r.t $x$) works very well.

Joe Shmo

you don't get a grader to do the dirty work?

Balarka Sen

17:35

Ted Shifrin

I did have an undergrad grader for that course, yes. Graded all my homeworks for upper level courses and grad courses.

Akiva Weinberger

@AlexKChen Argh, that's almost homogenous

Joe Shmo

nice! is that a grad course or an upper level undergrad course?

MatheinBoulomenos

We derived Cardano's formulas via Galois theory in a hw problem, that was kind of cool. Made the proof that solvable Galois group implies solvable by radicals more clear

Joe Shmo

its a lower level course in my grad program

Ted Shifrin

17:36

Neither. Officially it was upper-division, but most of my students were first- and second-years.

Akiva Weinberger

@MatheinBoulomenos That sounds like an interesting homework problem

Joe Shmo

first and second years grad? undergrad?

Akiva Weinberger

Was it the multipart, walk-you-through-it type? @MatheinBoulomenos

Ted Shifrin

Your course is assuming people know linear algebra and multivariable calculus — my course taught all that stuff plus the theory.

Joe Shmo

im lucky to have taken proper lin alg last semester

Ted Shifrin

17:37

Yeah, it's amazing how many crap linear algebra classes there are ... :(

(Not that I have anything against computations ...)

Joe Shmo

yeah.. my first undergrad lin alg course was garbage

Akiva Weinberger

What the hell is this

MatheinBoulomenos

@Akiva no, but we had a hint to look at the proof of the thing I mentioned. You basically had to take a composition series for $S_3$ and then work through the proof explicitely

Joe Shmo

i didn't understand that point of mathematics until late in my undergrad career

it was all computation, computation, computation

ÍgjøgnumMeg

My linear algebra course was just matrix and vector computations

"linear algebra"

Ted Shifrin

17:39

My second book was a "first" linear algebra course, but with proofs (and, of course, the obligatory "Geometric Approach").

MatheinBoulomenos

@ÍgjøgnumMeg that's useless

ÍgjøgnumMeg

@MatheinBoulomenos Yup.

0celo7

Linear algebra is shameful at my school

MatheinBoulomenos

Linear algebra at my school covers more abstract algebra than some abstract algebra courses, lol

0celo7

Combination of the Engineering college throwing its weight around and a prof who decided to put all the lectures online and not do class

ÍgjøgnumMeg

17:40

My university just.. assumes all undergrads will go into data analysis or finance

MatheinBoulomenos

(I should add that in Germany, high school students spend quite some time doing linear algebra geometrically in $\Bbb R^3$)

0celo7

there's an honors which is slightly better

Balarka Sen

Hot take: Linear algebra should be taught after differential topology and vector bundles

Xander Henderson

No.

Just no.

Ted Shifrin

I'm not arguing for an abstract course. I'm arguing for incorporating proofs in a reasonable and educational way. And for emphasizing concepts — we learn algorithms for finding basis for nullspace, row space, column space, etc. How do we use those to answer actual questions?

bolbteppa

17:41

Hot hot take: linear algebra should be taught without linear operators

Ted Shifrin

No, @Balarka.

Joe Shmo

it was never as apparent to me how detrimental engineering departments can be

0celo7

@BalarkaSen linear algebra is a trivial consequence of basic functional analysis

ÍgjøgnumMeg

Linear algebra without matrices

Ted Shifrin

Completely a horse after the cart, @Balarka.

MatheinBoulomenos

17:41

@BalarkaSen basic arithmetic should be taught after introducing natural number objects in topoi

Balarka Sen

What if I told you

I learnt linear algebra that way :3

Ted Shifrin

@JoeShmo: There's nothing wrong with engineering. Engineers need to learn to think and problem-solve, too. They just don't have patience for abstract stuff with no point.

You're irrelephant, @Balarka.

Joe Shmo

but the proof is the point

0celo7

@JoeShmo athletics is worse

MatheinBoulomenos

@BalarkaSen I thaught that you said that you learned LA out of Artin once

ÍgjøgnumMeg

17:42

Abstract stuff always has a point; it's a basis for more pointless abstract stuff

Balarka Sen

@MatheinBoulomenos Yeah

Ted Shifrin

Not always, @JoeShmo. Look at the balance in my course (if you watch linear algebra stuff).

Balarka Sen

I learnt inner product spaces because I wanted to understand the intersection pairing :3

Joe Shmo

i skipped to lecture 24, differential forms

Xander Henderson

@0celo7 This is an alternative to "clearly": chat.stackexchange.com/transcript/message/42925703#42925703

Eric Silva

17:43

@BalarkaSen do you come from a weird bizarro universe

Ted Shifrin

Right, @JoeShmo, I know, and that's the second semester. There is some linear algebra that comes after ...

MatheinBoulomenos

@TedShifrin that was mostly the second LA course which introduced enough ring and module theory for the structure theorem of fg modules over a PID. The first course was purely abstract algebra, with an emphasis on proofs

0celo7

@XanderHenderson I am quite tempted to do that. I can't quite get the maximum principle to work, but some fuckery will do it.

Balarka Sen

0celo7 is making the right life choices

Ted Shifrin

Mathein: Our audience in the US is far broader than yours ... math majors are only a tiny portion of our students. But UGA did introduce an applied linear algebra class (with almost no proofs) and almost all the students are taking that now.

Balarka Sen

17:44

@EricSilva Oh I read the thing you sent me

MatheinBoulomenos

I see. We don't even have engineering students in Heidelberg

ÍgjøgnumMeg

Actually I learned most of my linear algebra through fields as and when it was necessary

Eric Silva

did u feel the vitriol

0celo7

@EricSilva Yo, did you see my torus thing

MatheinBoulomenos

I think linear algebra is a good opportunity to get used to the types of proofs in algebra, because the structure of vector spaces is so simple

and conjugacy can be taught of base-change etc.

Ted Shifrin

17:46

I totally agree, Mathein.

Balarka Sen

It was a good article. Probably more aggressive than it needed to be but understandably so

Eric Silva

@BalarkaSen i think being over aggressive was almost the point

Daminark

@MatheinBoulomenos I've already linked the nlab page about what it really means to "carry the one"

Balarka Sen

Perhaps so. For me it's a good summary of why "woke feminism" is fundamentally flawed.

Eric Silva

or the banality of wokeness as a general concept

Xander Henderson

17:49

the word "woke" bothers me

Daminark

If you're just woke and you're not woke af, what are you doing?

2

Eric Silva

fuq i should sign up for the GREs

Xander Henderson

woke almost finite?

Balarka Sen

Daminark be thonking some serious questions now

Xander Henderson

what do AF $C^\ast$-algebras have to do with wokeness?

MatheinBoulomenos

17:50

mercio

o..o

Daminark

@XanderHenderson if you need that question to be answered, you're sheeple and need to wake up

Xander Henderson

@EricSilva A bit of life advice: study for the math subject GRE

Eric Silva

@BalarkaSen i guess it's always important to hammer on the point that it's not wokeness that's the problem, it's the lack of critical self reflection

@XanderHenderson oh yeah i have been

MatheinBoulomenos

GRE was the calculus test that determines if you can go to grad school, right?

Balarka Sen

17:51

@Eric well that's pretty much what the popular notion of woke has been for the last decade

Xander Henderson

my strategery was as follows: (1) realize that several of the schools to which I was applying required the subject GRE, (2) register for the exam, (3) sit the exam two weeks later

Eric Silva

@BalarkaSen i thought it was social consciousness

Balarka Sen

but i agree with you

Xander Henderson

I got into one school that required the exam, and all of the schools that did not

Eric Silva

which is good, but not without that necessary step of self criticality, otherwise it's pointless

Balarka Sen

17:52

@EricSilva As literal meaning of the word, yes, but it's really social consciousness slapped into a label of shallow ideology than anything

Eric Silva

i suppose so

Dattier

18:05

Let $P$ polynomial in $\mathbb Z[X,Y]$ with $P(4,3)=P(2,4)=P(4,4)=P(1,2)= P(1,3)-3$.
Is-it true that $\exists R,Q\in \mathbb Z[X], P(X,Y)=R(X)+Q(Y)$ ?

Semiclassical

18:20

@EricSilva I guess you could call it ideology as fashion/branding rather than actual belief?

Though 'belief' doesn't necessarily imply self-criticism either I suppose

Eric Silva

idk man ideology is a spook

the universe is a cruel and vexing puzzle

Semiclassical

yeah i dunno

Eric Silva

i just registered for the math gre and it induced an existential crisis

rip

0celo7

@EricSilva when is the deadline for the next one?

Daminark

Ugh I should do that but I'm not looking forward

Semiclassical

18:24

@0celo7 fyi, my main holdup with the code right now is that the RegionMeasure step is running into problems in some cases that I think should work

0celo7

omg, why are you spending so much time on this

Semiclassical

i dunno

i get too obsessed with these things

0celo7

I mean, I appreciate it, but you really don't have to

Semiclassical

yeah, fair enough

Eric Silva

@Daminark i have to read nietzsche later for class so today is gonna just go even further downhill

rip

0celo7

18:25

my prof was amazed by the 1D version

Daminark

F

I'm probably just gonna work on algebra and wait until Charlie uploads something

Eric Silva

i guess i should study for the GRE more regularly starting now

Silent

@AkivaWeinberger Sorry for so late comment, but if we need $\alpha_1<\beta_1$ to make sure $P_1+\ldots+P_{m_1}>\alpha_1$, then, wouldn't $\alpha_n=\beta_n$ would work, instead of $\alpha_n<\beta_n$?

Semiclassical

@0celo7 it comes down, of course, to mathematica being somewhat smart at doing integrals over regions.

0celo7

what's it integrating?

Semiclassical

18:31

just $1$ over the region of interest.

that's all the region measure is, after all

ÍgjøgnumMeg

@MatheinBoulomenos Braucht man bei euch die Abi-Noten um sich fürs masterstudium zu bewerben? Hab irgendwo gelesen dass man das in Deutschland gar nicht mehr benötigen darf lol

0celo7

@ÍgjøgnumMeg good god why would anyone care about that for graduate school

Semiclassical

the main trouble I suspect is that, while we're telling it to do it with NIntegrate, it's still trying to do some kind of symbolic preprocessing. I've run into issues with that before

ÍgjøgnumMeg

@0celo7 I know... but according to the websites in several unis, they want that shit

@0celo7 and I've lost mine so I need to pay like 100 pounds or something to have them replaced so I can apply for grad schools

0celo7

pounds?

Last time I was in Germany, they didn't use pounds.

ÍgjøgnumMeg

18:37

I'm from the UK lol

0celo7

How do you have an Abitur then

You mean the UK equiv?

ÍgjøgnumMeg

I do indeed mean the UK equiv

lol

0celo7

ok fair enough

ÍgjøgnumMeg

Don't think any unis in the UK care about A-Level grades, not sure why they care so much in Germany/Austria

MatheinBoulomenos

18:59

In Germany they care about your abitur if you want to study something like medicine or psychology, but few people want to study maths, so the grades don't really matter

Transcript for

$Mathematics$ Mathematics