Physics : How do we know an object is 300 lightyears away ?? Without assuming original color ?

For more known stars you can use cephid variables but I think otherwise it's parallax angle.

(That may be completely wrong)

Too far for angle trig I think

@Faust What monthly instalment will discharge a debt of $2455 due after one year at 5% per annum simple interest?

Then?

Anyone

Hey @SamuelYusim

$s(a)s(a)=s(aa)$

$s(a)=s(aa)(s(a))^{-1}$

$s(a)s(a)=s(a)s(aa)(s(a))^{-1}$

Therefore $s(aa)=s(a)s(aa)(s(a))^{-1}$

wait a minute, the squareroot map preserves conjugates?

@KanwaljitSingh its saying that you borrow x dollars and have to owe 2455$ dollars less after one year but you have to pay interest of 5% yearly (i belive this is correct?)

is so a cheap answer would be 2455/12

you borrow 2455$ pay it all back monthly before the intrest compounds

but i may still be misunderstanding the question

the question probally means simple interest is daily

Morning @TedShifrin

anyway i can probally help if you define all the necessary parameters

Aw man some nerds

How's it going everyone?

ex discharge debt probally means debt reduced by after paying intrest and simple intrest is daily monthly or yearly

@Daminark Hi

Morning @Daminark

@Daminark Hey hey hey

@CesarEo why did you delete your valuable answer? I think it was helpful math.stackexchange.com/review/suggested-edits/1015573

(wasso wasso wasso wasso aaaaa bit conneeeect)

?

@BalarkaSen No.

@BalarkaSen Have you seen schmoyoho?

@BalarkaSen Did you sit a bunch of entrance exams recently?

I love the thumbnail

@CooperCape Hm, I don't think so. What is it?

@TobiasKildetoft Yup I did

Any idea how it went?

@BalarkaSen guy is way too excited about something

@BalarkaSen They make a lotta memes into a song.

And mr. bitconnect comes up a lil'

@CooperCape Ah I see. I have seen some of those channels

@TobiasKildetoft I think I'll get in at least one of the two universities I applied for

that's good

isn't two a low number of places to apply?

@BalarkaSen is it very competitive in India? I think in Germany you don't have to take an entrance exam for a math BS at any uni

I scored 17/30 correctly in the multiple choice bit in the exam I'm hopeful for, and did 6.5/8 in the essay-type question section. I think the multiple choice score is just about enough to make the cut-off for the screening

Has anyone had experience with Strang's linear algebra book? I'm trying to choose a book for the LA course I'm teaching in July.

Also Hi @TobiasKildetoft @BalarkaSen @Daminark @Faust @Antonios-AlexandrosRobotis

hi @MatheinBoulomenos :)

@MatheinBoulomenos Hi

@TobiasKildetoft Yeah but there's not a lot of universities in India which has a decent mathematics syllabus. The number is exactly... 2

lol

@MatheinBoulomenos Yeah it's super competitive here. It kinda sucks.

beeeet conneeeeeect

@Antonios-AlexandrosRobotis use Hoffman-Kunze! Upside-down smiley face

@BalarkaSen Really only 2? Would those be like CMI and Tata?

@Antonios-AlexandrosRobotis gilber strangs book was used at my university the students considered it to the worst textbook ever can link alot of ratemyteacher posts

@Daminark i.e. ): or (:

okay, good to know

I'm trying to find a good "first course" in linear algebra book

@Antonios-AlexandrosRobotis be sure to work over arbitrary fields. Just $\Bbb R$ and $\Bbb C$ is boring

@TobiasKildetoft Wow, how do you know about CMI? It's CMI and ISI actually. Tata (or TIFR) doesn't take undegrad.

@Faust I think most linear algebra books are considered the worst ever by most students

@BalarkaSen QGM where I did my PhD had a major exchange program for some time with those two

@MatheinBoulomenos These students probably won't even have a good grasp of calculus, let alone what a field might be.

I learned what a field is in my first LA course

if you notice at the begining of the book the example showing how to multiply two matrices together it doesnt matter in what way you combine the operations you always get the correct solution making it completetly useless as an explanation as several incorrect ways work for the special case. @Antonios-AlexandrosRobotis

But it was near the end of my PhD so I didn't see much point in spending a month in India just finishing writing my thesis

@TobiasKildetoft Ahh nice. I knew CMI had an algebraic conspiracy going.

@TobiasKildetoft there are sevral posts on ratemyprof that suggest student used other books for the course cause gilber stangs was so confusing

I'm going to visit TIFR for a month in June (so next month), actually

@BalarkaSen QGM does not do much algebra actually

conspiracy

thought its a fine book if you already know LA and need a review

@MatheinBoulomenos things are different here. The understanding is that "intro" linear algebra is a course to prepare people for not only math but also physics, economics, etc.

close to no algebra at all really now, unless you count some weird stuff

Huh

I know that Tata holds some important conferences, right? Or so I think because I thought that's where those lecture notes come from (I may be wrong)

@MatheinBoulomenos seems like the course in question is one that's just "row reduce this" and "find the eigenstuff"

@MatheinBoulomenos Yep, it holds some international conferences.

you can do that in two weeks

@Antonios-AlexandrosRobotis i like Ted book A geometric approach to linear algebra as it give alot of motivation but non math people may not like it as much

@Faust is that book not very expensive?

There was one about algebraic cycles in 2017, I think.

India is full of algebraists man

@MatheinBoulomenos I can do it in one day, but if no one understands, why bother?

@BalarkaSen yeah, let's just pretend that algebraic cycles is an algebra thing (that might almost make some people at QGM do algebra)

@Antonios-AlexandrosRobotis think my hardcover was around 70$

(not that any of them do anything with algebraic cycles that I know of)

Algebraic geometry = algebra

fite me irl

I definitely agree but it seems like grad students probably don't get much jurisdiction over curricula

@Faust 0_0

This is why libgen exists

My favorite LA book is a German one that does modules and exact sequences in the first chapter. I have a feeling that it's not quite what you're looking for

That's kind of expensive. I'll have to keep investigating. Axler's book is free online, but it's too advanced for them.

@MatheinBoulomenos I'm quite partial to Manin & Kostrikin, but that is of a similar level of difficulty haha.

@Antonios-AlexandrosRobotis axler is alittle rough for a first course and as a second course its missing something

@BalarkaSen arxiv.org/abs/1510.07588 is probably the closest to algebra by someone currently (officially) at QGM

@MatheinBoulomenos Somehow that doesn't surprise me

lol maybe I'm stuck with strang, we'll see.

@TobiasKildetoft Interesting. So is there any focus towards a specific flavor of math that's present in QGM?

@Antonios The upside down smiley I had in mind was more like this

If Axler's too hard then Hoffman and Kunze is probably also too hard, much as it's objectively the best of all time

@BalarkaSen The centre is based around a huge grant for studying quantization of moduli spaces and the various things related to that, which includes a bunch of mathematical physics as well as some more algebraic stuff like quantum groups

And they used to have an actual algebraist, but not any longer. And Arkhipov used to be more algebraic and did some stuff with Lie algebras and quantum groups. But now he is moving to more geometric stuff

(and I am only unofficially a part of QGM, so I don't really count. They just adopted me when I returned)

one of my profs here who's a crazy algebraic geometer tought some tough stuff in Freshman algebra. Like chain complexes and the long exact sequence in homology associated to a SES of chain complexes. And he did generalized quaternion algebras which is something that usually only comes up if you want to compute the 2-torsion in a Brauer group. But his treatment of generalized quaternion algebras relies on twisted tensor products which is something I haven't seen anywhere else

there were some exercises like: alright, compute the homology of this Koszul complex

@Daminark see the frustrating situation I'm in is that the students just want easy A's, and my ability to keep working in similar teaching positions is a function of the evaluations I am given. A difficult course leads to bad evaluations.

I don't want to give easy A's, but I also want to eat.

bad spot to be in with that book

I don't think anyone here cares for evaluations of students or how many students pass the course

our university changed our book for basically what your describing

what is a twisted tensor product to you?

@Mike lmao, for me your message showed up a second before your icon logged in

@TobiasKildetoft I see.

Probably most of the research (at least by the centre director) comes under the heading of quantum topology.

that's funny

@MikeMiller suppose $A_1$ and $A_2$ are two $\Bbb Z/2\Bbb Z$-graded algebras over a commutative ring $R$, then the twisted tensor product $A_1 \otimes_R^\varepsilon A_2$ has multiplication defined by $(a_1 \otimes a_2) \cdot (a_1' \otimes a_2) := (-1)^{|a_1'||a_2|}a_1a_2 \otimes a_1'a_2'$

@Daminark Maybe he is a time traveler, let's see if he answers the question I'll post in 5 minutes before I do!

ah sure

this is again $\Bbb Z/2\Bbb Z$-graded

you see that in clifford algebras or in dgas

that's the answer to Alessandro's q

I don't know much about that beyond definitions

it just seems like a weird thing to do in freshman LA

For sure

Not much value to it there

well, he did do Grassman algebras and Clifford algebras after that

Still, who gained

He defined the Grassman algebra as the Clifford algebra for the zero bilinear form and his proof of the existence of Clifford algebras used twisted tensor products and then he used the functoriality of the Grassman algebra to define determinants

so ultimately, his definition of determinants relies on twisted tensor products

rip

still a better definition than just writing down the Leibniz formula

more interesting at least

@Alessandro where's the question? It's been more than 5 minutes! >:(

@Daminark Turns out I didn't have a question

So I guess that technically Mike answered all of my questions

technically correct is the best kind of correct

now you should give Mike a vacuous upvote and a vacuous bounty

It seems weird to me that I answered a question with 5 favourites about 9 months ago and there has been no comment, upvote or accept

My weirdest was someone unmarking an answer as answer ~~6 months after they marked as answer.

and the asker is still active

Yup

oic

bummer

maybe it's because I used the structure of the multiplicative groups of local fields? But that's not something I can prove in a single MSE post and I gave a reference

@MatheinBoulomenos It's always very unsatisfying

You feel like you've worked hard on an answer and nobody cares

yeah

But at least we all share that dissatisfaction :)

yeah even hearing some feedback that something isn't clear would be more satisfying than that

I also got downvoted once for using the Lefschetz fix point theorem. Because apparently that's some esoteric advanced stuff you can't assume for questions tagged algebraic topology ...

Nowadays I just occasionally click the questions list and answer most things in the comments to not deal with that

Or just don't engage unless something's really interesting

Should I email someone if I find an error in a past grad school qualifying exam? I occasionally use this if the standard exercises are too boring and I found an error that cost me quite some time where I tried to prove a wrong result. Maybe they'll reuse those?

probably @MatheinBoulomenos

I would've been pretty pissed if that was my actual exam

@MatheinBoulomenos Yeah, if nothing else they might use them for having the students practice

in which case it is also good to know about an error

I had one of the grad students look over the exam for the coming reexam in algebra, and fortunately he caught a major error which made one of the exercises wrong

The thing is that was a type of exercise which I'm really comfortable with since I practiced those over and over, so if that were my actual exam I would try that question over and over and get pretty demotivated

I know that one should probably move on in that situation and get not stuck on a particular problem, but come on, if I can't solve that, then what can I?

@TobiasKildetoft do you happen to know a simple proof that groups of order 720 are not simple? All the proofs I've seen have been pretty difficult, a lot more than other "groups of order $n$ are not simple" results

Someone at UCLA made a calculator that spit out proofs of the nonexistence of, or lists of, the simple groups of a given rank, up to 1008

I've been thinking about something like that

do you have a link?

Unfortunately it seems to be down and I asked him about it a while back and he said he doesn't have the code anymore

ah, too bad

I need to play with spaces like Mathein does with simple groups. I feel like that's the advantage of good algebraists: they have a lot of examples in their hood

I don't think I nearly think about as many examples

Hello, guys. I'm searching for a definition. Let $I$ be a closed interval, say $[0,1]$. Let $\{\Sigma_t\}_{t\in I}$ be a one-parameter family of surfaces in a 3-manifold $M$. What does it mean this family to be smooth? I.e, what does mean "the family of surfaces vary smoothly with the parameter $t$"? Is there such a notion?

I really like surfaces

@AndersonFelipeViveiros think about them as maps $\Sigma \times I \to M$ which are smooth and embeddings for each $\Sigma \times \{t\}$

@MikeMiller Me too.

@AndersonFelipeViveiros It means there is a map $W \to M$ from a 3-manifold with boundary $W$ such that $\partial W = \Sigma_0 \cup \Sigma_1$, I think. The "slices" of $W$ are the surfaces $\Sigma_t$.

That's a good interpretation but only if you want the topology of the surfaces to change in this family which depends on context

($W$ is actually also foliated over an interval, but whatever)

All this seems reasonable.

@MikeMiller Yeah good point it wasn't clear to me that was the case

context?

@BalarkaSen with a singular foliation

Best to think of it IMO as a $[0,1]$-valued Morse function sending boundary to boundary

Ya I was hesitant to say that

That works

I think foliation people call that a "Morse foliation"

@MikeMiller I think they can change their topology. It's the context of sweepouts

Can you link people the thing you are reading?

tftw when your problem in the algebra qualifying exam starts with "Let $\mathcal C$ be the category semi-symplectic paramonoids of Rice-Paddy type, satisfying the Mussolini-Rostropovich equations at infinity"

A lot of people who weren't strong in English got upset about that problem because they interpreted it as terms they don't know and were too embarassed to ask

the question is pretty easy though

speaking of examples - what are some good examples of applications of characteristic classes to keep in mind? off the top of my head i know e.g. immersion of real projective spaces / complex structure on spheres, some things about cobordism etc..

@MikeMiller oh, you're from UCLA, right? do you know whom I should contact for errors in the past qualifying exams?

I am sure they (and all of us students) know

@loch In low degrees/dimensions I use them as a classification tool, e.g. rank 3 oriented bundles over a 4-complex are classified by $w_2$ and $p_1$

But from an algebraic perspective Quillen's calculation of the cohomology of $GL_n \Bbb F_q$ with coefficients in a prime field $\Bbb F_\ell$ of different characteristic, and hence/also the K-theory of $\Bbb F_q$, is done via characteristic classes of vector bundles over $BG$

-

0.3

.3

+-+

he uses Brauer lifting to make a space $F\psi^q$ which represents "complex vector bundles with $E^{\otimes q} \cong E$" (whatever that means, and it's a bit of a lie), which naturally come from $\Bbb F_q$-representations via Brauer lifting, and then uses the cohomology of this space to get cohomology classes on $BGL_n \Bbb F_q$

@MatheinBoulomenos we especially know it if you're thinking of the question characterising epimorphisms in topological spaces

@loch they're also show up in obstruction theory e.g. the existence of spin structures or spin-c structures; they're related to Steenrod squares on closed manifolds, and one can often be used to calculate the other

I was drinking some carbonated apple juice and made a bet on how carbonated it could have been. Gave it a shake in it's bottlecapped state, and the bottle exploded on my computer keyboard. I won the bet.

@MikeMiller oh yes that i've seen a little bit of

@loch Yeah

to group cohomology

I think it's not something general, and it's just a low-dimensional piece of luck - albeit one I use all the time. It's about the difference between homotopy classes of maps and their induced maps on homology

i see - seems like a good repertoire of examples to keep in mind -- thanks!

I have yet to understand characteristic classes

The axiomatic approach looks magical to me

@BalarkaSen I asked about your dp .. but anyway, did you give any entrance exams?

Ah, I guess rationally you might like the point that the Chern character $K(X) \otimes \Bbb Q \to \oplus H^{2k}(X;\Bbb Q)$ is an isomorphism of rings

Jee/cmi/isi anything?

@Sawarnik What's a dp. Yeah, I gave ISI and CMI

Oh great :) .. how was it?

I think for rational KO-theory you get a similar thing in degrees 4k via a Pontryagin character

And where are you going?

I think I'll get in ISI

As in, which university I'm going in? idk man just wherever I get in

Dp means profile picture ... isi banglore or kolkata?

Oh, the former. B.Math is taught in ISIB, not ISICal

How is "Dp" an abbreviation of "profile picture"??

Oh, Display Picture. Fuckin' hell

Well, there's a quite good chance i might end up there too!

Could be double-p

LOL

@Sawarnik Nice!

Though will wait for jee results, some IITs have good math programs ... but then jee didn't go that well :(

Sorry to hear. The Indian admission procedure is soul-crushing.

No I guess its same everywhere .. competition is so intense.

Should be present in all countries i guess

@AndersonFelipeViveiros Specifically in the context of sweepouts I think it definitely means a smooth map $S^1 \times I \to M$. It may not even demand that the individual curves are embeddings

Uk seems on the whole chill af when it comes to uni admissions.

I had a relatively easy time of uni admissions

My impression is that most countries don't have a competitive admission procedure for undergrad.

It's a standardized SAT score + recommendation based game in US, if I understand correctly

Oh right .. france has one though, was talking to hippa

Oh yeah France is hell

@Sawarnik I think the Indian admission system has done a good job of perfecting the stress of the process. While it probably produces "only the best" workers in the end, it crushes many on the way in.

You didn't give JEE at all?

Nope.

@MikeMiller Individual curves? Do you mean surfaces?

Oh wow the divisibility rules for $9$ and $11$ just come from the fact that they're 1, resp -1, mod 10, and you could easily play the same game for 19, say

@AndersonFelipeViveiros Oops, I googled a bit and saw people talking about curves-on-surfaces. My apologies!

I am easily confused

No problem! ^^

Haha, it's ok.

@mike Don't know, I have made peace with the process .. ultimately how much work you put in the results come out accordingly .. the problem I think is that relative to our size the number of good quality seats are very low.

@BalarkaSen why not CMI though?

@Sawarnik I think meritocracies cause a lot of psychological trauma. In academia in the US 40% of grad students are depressed and anxious.

Of course, your point is well-made that this could just boil down to the problem of too many people vs not enough positive outcomes. But I think that's inevitable.

Yeah, that's what i think. Its mostly inevitable.

...in the structures we have created. :)

I don't think there is any strong correlation with grinding for test scores and interest, and as long as the latter isn't concentrated on it'll continue to crush people under power-hierarchies.

@MikeMiller maybe one should say the myth of meritocracy

that's fair

@Sawarnik It didn't go as well.

Hmm, there's half a chance i may get selected for cmi, should be getting just about the cutoff.

How many subjective problems did you do?

I thought there's no official cut-off for CMI

There isn't but some cmi people say its about 55

Technically 3-ish. I wrote down my approach for the other ones, and why some of those ideas won't work.

I asked r9m and he said it was about that in 2012 .. though the format has changed.

Meh, I enjoyed the test. I don't think I'll get in, but also fuck it

I did 3 too, almost did the geometry too but couldn't write it down.

I know someone who did a solid 3 (of the hard ones, which has 15 points each) but didn't make it last year.

Yup, the test was nice :)

Ah, then I'm out lol.

Isi then.

@MikeMiller nevermind, it was from some other grad school, I confused that since I looked at past exams from multiple schools

There was one that asked to find a non-surjective epi I think

But they wanted the category of hausdorff spaces

rip

yeah

I thought that when I saw it

since after $\Bbb Z \to \Bbb Q$ that's one standard example of a non-surjective epi

@mike Ultimately, there has to be some testing through which the admissions will be done, its just bound to create stress. Maybe the US system handles it better..

there is no admission process at all for math undergrad in Germany

That's weird :/

you can even get into most schools if you barely passed your highschool math exams

@Sawarnik The US has far less population and no craze for a particular university for undergraduate studies

@sid yeah, that's what I said about there being more good quality choices in the US.

@MatheinBoulomenos Boon of having lower population

The solution is to lift the gun law in India

@MatheinBoulomenos So the univs that are ranked higher, how do students get into them?

Some sort of testing must be there?

no

you have to have the equivalent of a high school degree

That's all?

Interesting

It's the same in Italy (with an exception or two)

@BalarkaSen I wonder if guns are made legal for teenagers to have in India, would the suicide rate increase?

yes

ncbi.nlm.nih.gov/pmc/articles/PMC478945

@Sid in terms of population density, Germany has a lot more population than say, the US

the moral of the story being that suicide rate has a clear link to availability

population density of US is far greater than India too

really?

@BalarkaSen Definitely not

@BalarkaSen The US has a lot of empty space, how's that possible?

I also feel that there's a lot more school elitism in the US than in Germany. For undergrad, the choice of school doesn't really matter except maybe for the advanced courses you can take in your final year. Nobody really cares much from which school you get your bachelor/master/PhD from

Ah I was comparing the peak of the popular densities of the two countries

woop

of course, for masters and PhD there will be different schools specializing in different things

I would say that I did not see a major difference in "average ability" in the undergraduate students between when I was at my 50%-admit undergrad and UCLA

(There is still an admissions process in the US and it's pretty stressful from our perspective but the education industry, calling it what it is, is so gigantic now and the value of a Bachelors so opaque that you will probably get in somewhere and do ok going to most schools, unless you're then looking to go to higher education)

there's a massive difference in the uni i took classes at in HS when i lived in florida and where i go now

but maybe it's cuz this school is small by comparison, self selecting, and for crazy rich people

there's a difference in instruction but to my mind mostly at the higher levels of it