@Juliamisto yes

Finished undergrad starting new job

🎉 congratulations

Feel sad tho wasn't able to get much math I had to switch from BS1 to BA which meant more general studies :(

You can always study math on your own.

That is true I'll have to head back to home uni to farm my gpa for grad school tho

It'll also give you time to develop mathematical "maturity."

That is true :) the issue is that the a&h courses just ate up the rest of my credits

I only took like Calc 1-4, Linear Algebra, Real Analysis I, Linear Algebra I, Abstract Algebra I, Differential Equations I, Functional Programming/Algos I, Intro to Machine Learning, Honors Independent Study like 3 times

And I was told when I had a european guy look at my transcript that I hadn't done enough

I didn't know where you are, or what those classes are, but just looking at course titles, I'm not surprised. You have maybe two or three (possibly four) classes which appear to be upper division. And there is no real concentration or the to those classes.

I went to IU Bloomington which is a good university it was mainly due to financial reasons to finish up BS1 would have taken 2 more years and I didn't have the money

In the US, I would expect topology, at least one more course in analysis or algebra, maybe some set theory or number theory.

I didn't know what bs1 means.

Bachelor of Science

bulletin.college.indiana.edu/programs/4235/MATHBS1

Most of the top students in the program I was at was already hitting graduate courses already

Isn't Ciprian Fois at Indiana?

Also, I still don't understand what the 1 in bs1 means.

For what it is worth, my undergraduate degree is a ba in math.

Yeah Ciprian Fois is at Indiana

@XanderHenderson the 1 means it's the premier program

Though at my undergraduate institution, the difference in a bs and a ba was a foreign language. I took Russian, rather than CS.

Oh, shit! Fois died!

Yeah a while back ago I just remembered

RIP

He was my masters advisor's advisor.

Oh wow o.O

at least everyone remembers how to spell his last name

Still I feel like I don't have enough background and that I wasted too much time on other things

Man, that sucks. He was a cool guy.

@leslietownes I got it wrong, didn't I?

:)

I know how to say it, not spell it

with romanians you often have to choose one

Foish. With a good Eastern European / Yiddish "oi" in the middle.

Did he work in fractals?

I'm not even happy to hang my degree on the wall

the Degree of Shame

(Shame)°

in all seriousness the ba/bs/whatever distinction is basically meaningless outside of specific institutions, many places only offer one or the other in a given subject, so nobody can really keep track of whether/where 'bs' is the 'harder' degree

@user85795 not really. More operator theory/ PDE stuff.

anyone skimming your transcript for grad school would be looking more at substance than titles

I think he had some ideas about Navier-Stokes.

Still my grades are terrible and my gpa is barely at a 3.0 I'll need to do a lot of grinding before trying for grad school again

@leslietownes This. People want to know what classes you took, not the name of the degree.

👍

@Zophikel By the end of my second year of undergrad, I had a 1.9 GPA. I managed to get that up to a 3.5 by graduation (like, 8 years later).

My grad school strategy was to complete a master's, first.

Then apply to PhD programs.

@XanderHenderson my plan was just to grind out more courses at the advanced undergraduate and graduate level then try for graduate school

Now that's a lot of "grinding."

Also, in terms of GPA, your last two years matter more. And courses in your major master a lot more.

@user85795 To be fair, I took three years off in the middle to work and train in foil.

@Zophikel if you can afford it. It typically costs less to take classes if you are enrolled in a program. And if you are in a masters program, you might get work and tuition waivers as a TA.

@XanderHenderson yeah there is a slight issue for things like scholarships and etc they use your undergrad gpa to determine candiacy

Like some of my math grades are bad I got a C in Analysis I and was close to getting a B

That's rough.

So going and doing a Masters may not have boosting effect you might think and masters is getting more common as well it would have to be a super tier leveled place at least

No one REALLY cares where your get your degree, except at the most elite level. It is more about who you worked with and what you produced.

But low grades in math classes makes things harder.

@Jakobian Fair in principle, but what can I say in practice about finding the $q$ which $p$ doesn't divide? Is that beyond the scope of what I should be able to deduce?

@Zophikel this feels like it would depend on the school, and not be a general property of masters programs.

but yeah, there isn't really a "lane" for people with low grades in stuff like analysis to just join and go to grad school, one would have to make up a kind of personal thing instead of just following a template

And all the places I've interacted with give all their grad students funding as best they can, regardless of undergraduate GPA.

Grad school funding is very different from the undergraduate scholarship grind.

i know someone who went to a masters program in an applied area and then kind of 'lateraled' back into math for a phd, but they had to be pretty creative about where they went and there was a lot of stuff they did that isn't, like, replicable in the way that "get all As, take the GRE, apply to random places" sort of is

@leslietownes regardless I need to improve my profile and just focus on math/cs more during undergraduate I had a lot of difficulies with the arts/humanities and I should have just focused on math more

@leslietownes yeah, that's the problem. But if you can fill in the gaps and demonstrate ability, it may help.

yeah totally

@leslietownes what did they do ?

they went to a masters in an applied program that was co-run by someone who knew a math prof they worked with in undergrad and then did a mathy applied thesis and applied to phd programs at schools where people they had met during their masters study were researching similar stuff

so, not at all weird or impossible, but just very "custom," i.e., not just turning the crank on some kind of program and leveling up

👍

My other upper division courses were fine and my grades improved over time it would have taken 2 more years at the rate I was going to recover

@Zophikel that's what I did.

Graduated high school in 99. Completed a BA in 09.

Then took two years off and taught high school and middle school. Then finished a Masters, then a PhD.

@Jakobian I see, and I guess if I wanted to tidy things up I could choose different $N$ at the start

This question and answer provied some insight

Reminds me of the best theorem in Hubbard^2: "elegance is not required"

@XanderHenderson my only real concern is that I had a pretty strong disdain for liberal arts and the only reason I even bothered to work hard in my other courses was so that I can keep my scholarship and for other financial reasons. It seems like at top graduate programs everyone is insanely well rounded outside of stem and most of my issues were with having broad difficulties with humanities and social sciences at large

@Zophikel you should get over that disdain, if you haven't already.

The liberal arts are important.

That is true :'(

i dunno i sort of get it, if you are only exposed to intro classes where a lot of profs are checked out, the classroom experience might not be that great

so in the same way i wouldn't say someone outside of math needed to take three semesters of calculus because it was good for them, maybe i wouldn't big up the "general education liberal arts experience"

i'd just separate class stuff from, like, your own mind and attitudes about subject matter

in almost any department in almost any school you can find people who take things way more seriously and think way more carefully than you do

When I switched from BS1 to BA I had to like to things like history, etc at a higher level the issue I didn't really have things like a culture when in things like cultural classes I found it difficult to even related to the material.

there's also an element of, taking responsibility for your own education, meaning even if you're in a boring class where the prof sucks and maybe the other students are not inspiring or pleasant to be around (which does happen), can you nevertheless deal with that in a way that doesn't etch an F in your transcript, or whatever

i didn't get much of anything out of my general ed classes

Dont' get me wrong I was grinding the classes but I still found them difficult. Especially writing for those classes as well writing for something like english or history is different then technical writing I found it very madding

I was a humanities major before I was a social science major before I was a math major.

yeah, depending on the instructor the style of writing you need to adopt may not even be that good, objectively speaking. i wouldn't assume that an english major is 'good at writing' any more than i would assume a math major is good at mental computation

Wanna discuss the avante garde Soviet composers of the early 20th century?

if nothing else it's an education in adjusting to different contexts and figuring out how to navigate them

IN THE ORIGINAL RUSSIAN?!

that's a nyet from me

@leslietownes pretty much when I did history of maths which really just a history course I nearly failed the class due to my writing. Writing essays for that class was painful

@leslietownes По чему нет?!

zoph i totally get it, writing well is hard

For reference, some of the books on my shelves in the living room:

my day job is like 80% writing and most of it is objectively not that good, usually it is 'good enough,' literally everyone struggles with writing (or they're not paying attention to it)

I honestly wonder if I would have just been better off just grinding out math and ignoring everything else

Especially looking at myself now going through those classes didn't really improve my personal development in anyway so I'm still trying to figure out the value obtained from doing those courses

In any event, I need to sleep. G'night.

xander: that figurine at upper right is cursed

G'night

Regardless by my calcuations it's going to at least take me 40 credits to get back to a high gpa again

@Jakobian I've been trying to make sense of this for the last little bit. How are you getting that first inequality?

@leslietownes curious question do professors view themselves as public servants ?

maybe some of them do? i don't think it exactly comes with the job

I emailed Peter L Clark regarding my stats and he said I would just benefit from farming more courses he explained that his program in particular successes hinges more on general academics then pure mathematical ability. He mentioned that theres a lot of stuff you have to do outside of research that makes or breaks how successful research no matter how bengin it may seem

it was kind of him to do that. certainly many academics are maybe more likely than the average person to share their time and experience with anybody who shows an interest. maybe more in math than in fields closer to 'everyday life,' because it's less common that someome might show an interest and less potentially overwhelming if you do end up replying to correspondence like that

but a lot of people outside of academia are pretty generous with their time too, irrespective of any sense of duty to a larger community

I have a lot to work on the only issue is regarding affordability air forces tuition assistance hasn't kept up with the pace of inflation so i'm trying to get another swe/cs job

it's also pretty common for academics to have one set of rules of engagement for people who have an unusual interest in their narrow research area, another for people in their department at their school, another for people at their school generally, and another for the general public

@leslietownes it's from my understanding at least coming out of undergraduate that the more higher ranked the university the more they value culture which is why they want to see good grades in a&h courses

sometimes even prioritizing email from randos who are really versed in their subject over 'paying customers' in their classrooms

Oh XD

@Zophikel i think one attitude that you will find is pretty common, more or less anywhere, any department that has a grad school, is "our grad classes are harder than general ed classes that undergrads take"

so it's not that anyone cares very much about being well rounded in history, or whatever, but there's the thought of "this is some mass-administered thing that dozens/hundreds of people do every year, so it's kinda not great if someone gets a low grade in it, because 'anybody' should be able to get a high grade in it"

maybe as the reputation of the university goes up you get more snooty versions of that, but you will find that anywhere

i see pete clark's answer linked above kind of gets into this. universities generally employ who are Good At School

and that percolates into how they look at everything

I mean once I get 60 more credits in my gpa profile will look a lot better the issue is just now affordability currently I have one job and i'll have to get another

financial stuff is really difficult, i wish you the best of luck

even if you aren't in financial distress it is good to keep one eye on that sort of thing as you do whatever you do

my wife has a phd and although she did not go into debt over it, it was not really a financial step up, she is earning now what she would have earned if she had stayed in the kinds of jobs she had before grad school

which is fine, but maybe wouldn't have been fine if she had conceptualized of the academic journey as a financial step up

e.g. when you try to get a home loan people mainly care about your assets and income and not what degree you have :)

> so it's not that anyone cares very much about being well rounded in history, or whatever, but there's the thought of "this is some mass-administered thing that dozens/hundreds of people do every year, so it's kinda not great if someone gets a low grade in it, because 'anybody' should be able to get a high grade in it"

So it's mainly bout hitting metrics then @leslietownes ? I mean it would explain how people get into grad school by simply just farming courses after undergrad

well, i don't know if what it's "mainly" about, i think that varies. but generally, because academics are Good At School, if someone is applying to grad school it reduces a lot of perceived uncertainty and unpredictability in that process if they are also Good At School

it's what academics understand

pete clark is probably an exception because he has spent so much time involved in recruiting/advising/etc., a lot of academics just whisk themselves through undergrad in the expected 4 years and go straight to grad school and never work outside of universities and consequently often aren't that good at understanding people who aren't carbon copies of that

which can mean (among other things) that they are not actually that good at giving advice on how to do what they did. they followed a script, and someone who isn't on that script is outside of their experience and maybe their understanding

Ahh that makes sense now thinking about most of the candiates from top 30 onwards look the same 4.0 GPA won all the awards, etc

yeah i mean no disrespect to career academics, but in asking one for advice, it is sometimes helpful to think "as distinguished as their career is, would they really know about this situation." someone involved in admissions/advising probably would, but a random academic, probably not

The best advice I got was just to grind my iugpa and the lady said I would be fine

it's good to look predictable and conventional on paper

if there's weird stuff or stuff that needs explanation, it's best if that stuff is also on paper so you don't have to hope you can get someone on the phone to do it

What does an unusual candidate look like ?

grinding gpa is one way to do that, but imvho i don't know if a lot of math academics would necessarily know what to make of post-undergrad grinding that isn't grad school

it's more common in other fields (e.g. med school)

Doing that would be mainly to meet the admission requirements so my application dosen't get tossed out

always a good thing :)

I mean yes it's an uncommon move for math/physics but it would give me more time to learn things properly and be able to build a better foundation

What subject do you want to do graduate work in?

Comp Sci and Physics think something like nanotechnology or quantum technologies

@user85795 for example a program like this: gsas.harvard.edu/program/quantum-science-and-engineering not uncommon to see triple majors

niiice

Like fellowships like the Hertz foundation are looking for people who have interest in academic topics but are willing to work outside of academia

Which is why I was a bit sad during undergrad I wanted to grind more math's along with other stuffs like chemistry or even bio

the further you get away from pure mathematics, the further you get from anyone who might give a shit about your grade in real analysis

lol

That is true but the programs i'm looking at do involve pure math and the admission committee does look at that as well

it's definitely one of those kind of thresholdy, gatekeepy things, again maybe not because of any substantive reason, but because of the attitude that "what we do is harder than this"

but i think the awareness of the arbitrariness of that gatekeepy role increases the further you get from pure math

then again, you never know. i had a guy ask me a difficult limit in an interview for a purely legal job

did you get it right

:^)

yes but it turns out he had misremembered what it was and so we disagreed about the right value

weirdos are everywhere

@leslietownes that could be the case at least from the professors I've talked too in the US however at some point I can see this not working programs can't admit all qualified or overqualified candidates in this day and age. It would be understandable if they were reject someone with my profile due to the fact they want someone that can be a leader in and outside the field.

American education does not make sense

It is in the business of making dollars.

re: chemical (oil) engineers are the highest paid undergads

I can see why the advisor gave the advice she gave

Have you started looking at the content of the GRE.

Yes i've looked at it for now I wanna hit the courses and fill my mathematical gaps at least

There are like three uni's courses I can afford atm

👍

@user85795 there is something out there more harder then the gre or putnam that I want to do

damo.alibaba.com/…

@leslietownes That's a kachina. Traditional Hopi carving. Not at all cursed.

The only issue is like with residing in certain states for tax purposes I can camp out another state for a couple of days to be considered a "resident" so I can get nice prices

Still I want to improve my gpa in pure math at the very least before doing anything else

@Zophikel thanks for sharing 🙏

@XanderHenderson I see glimpse of star wars at upper left

@leslietownes what does an unconventional candidate look like for math graduate school ?

@SoumikMukherjee Lego Star wars for the Wii.

Seems i'll need to hit the early to advanced graduate courses and get my A's >:)

ooh

zoph: depends on the program, of course. at the higher levels (particularly phd programs) it is relatively rare for candidates not to have just immediately gone through a 4-year math program with good grades in it. departures from that (e.g. majoring in something else, e.g. having done a degree but not very recently before applying, e.g. middling grades) are unconventional

Video games and DVDs are on the shelf to the left. More books and magic cards are to the right. Most of my math texts are upstairs in my office, or on campus.

nice collection

i like the exposed brick

@Zophikel Many programs will help offset the out of state tuition for the first year, and will expect you to become a resident after that.

@leslietownes me too

The Complete Works Of Shakespeare caught my eye ;-)

@leslietownes my case was my grades were improving but I had to switch to BA which had wayy more general studies requirements and less math and struggled a bit due to my poor writing

Shakespeare is great. Though Marlow is better. :)

But I think he's still in a box.

@Zophikel well, it also doesn't sound like you are angling for a specifically math-only grad program, so i'm not sure how much of that might or might not apply to you. interdisciplinary programs tend to have broader reach, in terms of the people they draw from

why not shakespear to go with marlow and fois

I'm on mobile. Autocorrect ducking sucks.

@leslietownes the programs I'm aiming for are heavy in math but they involve another topic like physics or cs/ece

I should be sleeping... :(

zoph i understand, but i expect that in a lot of places, 'heavy in math' means something very different in the interdisciplinary context than it does in the purely math context.

e.g. my wife has a masters degree in statistics that she got as part of a social sciences phd. it was very 'heavy in math' to everyone in that program, but, had she applied to the stat department just to do a masters' degree they probably would not have admitted her. and the standards they applied to her work was very different from what they applied to their 'own' students

@leslietownes what are you imagining ?

e.g. she has never taken real analysis and it's possible that at least some of her instructors in the stat masters program had never taken it either.

quantum computing is heavy on the quantum side of things.

interdisciplinary stuff is just different, is all i'm getting at

I will be starting my PhD in this July ↖(^▽^)↗

@SoumikMukherjee FINALLY.

just kidding :)

@leslietownes Haha right:)

@leslietownes it's from my understanding that interdisciplinary stuff may or may not be rigorous. I've heard people say things like stats isn't rigorous

@Zophikel it really depends on the people and what they are doing. even within a single department/program you can never be too sure.

@leslietownes I can link you some of the programs that i'm looking at

some of the people my wife learned from in her masters program publish, like, definition-theorem-proof stuff, and some of them think you're a wizard if you know keyboard shortcuts in excel. the world takes all kinds

When I was interviewing in eastern europe for companies the guy mentioned that the average US student dosen't know much coming out

Which is why I'm somewhat worried @leslietownes at my current level I would got smoked if I were to even gain admission to a top25 program I don't wanna be due that hasn't done representation theory in their undergrad

a lot of european educational systems allow for earlier specialization, so an undergrad degree in many places in europe is more akin to maybe a masters degree in the USA. to paint with a very broad brush, there is less emphasis on "general education." i don't know that the schooling is actually any better

@Zophikel this strikes me as maybe reasonable if you were applying to a pure math phd program and maybe unreasonable if you are applying to some interdisciplinary but math-intensive thing. nobody gives a shit about representation theory

@leslietownes ahhh not quite it's important in Physics and Chemistry

yes and the 'experts' in that field have probably not taken the class on it in their pure math department.

if you don't actually have a background in physical chemistry and a grad program needs one, that's one thing, but i wouldn't expect the math department to be any of use in that.

Physical chemistry is more chemistry than physics.

there's like this whole world of pure math stuff which is just very specific to pure math. giving a shit about real analysis strikes me as maybe commonplace in math grad programs and maybe rare elsewhere, except just as a way of culling a list of applications from length N to length N/3.

Again, gate keeping.

@leslietownes to be more specific the programs i'm looking at are in Theoretical Computer Science/Physics and the specific departments research I'm looking at people doing things in quantum computing, condensed matter, chemistry, etc involves a lot of math's, engineering, etc. Like yes there is stuff that is specific to pure math but I don't think that is the case in this era.

Like at the early stage it's important to have some breath and that's one of the main weaknesses of my profile

Like Physicsts will stroll into a pure math department and mathematicans will do as well for interdisciplinary programs the prefect candiate will be able to understand the needs and motivations of both camps and be able to pivot their research accordingly

all of this is really program dependent. i would not even expect similarly named programs at places of similar status to have the same system of values in what they look for in applicants. i would recommend doing very individualized research on what specific programs are looking for.

I've only ready been doing that :)

I've already been doing that :)

"real analysis is important" is too vague of a vibe to base anything on. maybe that's the vibe at one place and SO not the vibe at another.

@leslietownes actually what I should have to be fine at most programs is the core pure math courses + (exposure to an applied topic at least)

For instance if I was heading to a Physics program I would need the other core physics courses as well

But with how competitive things are getting I need to do more then the bare minimum I need a very wide spanning mathematical background

yeah, the classes you described earlier seemed roughly equivalent to a minor in math at most american universities. the question is more whether a program is satisfied with that, or if it's like "well what grade did they actually get in X."

and is that some substantive thing where you actually might need the education, or are they just doing that to filter applicants. i honestly don't know. it wouldn't surprise me if two universities in the same town had polar opposite ways of approaching that inquiry

Depending on which department the funding is coming from.

C+, B-, C, B, B-, C+, C, D+, A are like my math grades

B in Abstract B in Linear B- in Comp Sci and the A is coming from an independent study

yeah, like, is that alarming, or totally normal? i think it would depend.

I would say alarming the grades are pretty inconsistent and I was taking them when I had to catch up on my other requirements

anyway, i would not assume that because an interdisciplinary field draws heavily upon X, that its practitioners are experts in X, let alone all got As in X in undergrad, let alone all care about whether you got As in X in undergrad. some of them might, but not all.

@leslietownes from the research i've been doing it seems like thats the expectation

I just checked my transcript I actually have one more A

in?

another indepedent study for math I did last semester

C+, B-, C, B, B-, C+, C, D+, A, A are my math grades at this point

I'll need to take the graduate versions of those classes to beef things up and go from there

@user85795 ^

But in summary yes @leslietownes I consider my situation a bit alarming I barely touched enough math I don't think most programs would be satisfied with my current results

Anyway g'night I gotta head to bed and get ready for today

@Jakobian yesterday we were talking about projection of matrices and you identified, topologically, the space of matrices with $\mathbb R^{mn}$. I have a hard time accepting this association. There is something called vectorization. In projecting a matrix onto one of its entries, did you implicitly use this map somehow? If we associate a matrix with a point in $\mathbb R^{mn}$, then I guess we have to vectorize it somehow.

I struggle with understanding vectorization...

Or is it always ok to think about a matrix as a point in $\mathbb R^{mn}$?

@psie its standard that topology of space of n x m matrices is given by that of R^(nm)

yeah, ok, I'll just accept it

When you ask about continuity of Df, what topology on the image do you have?

that of $\mathbb R^{mn}$, as you say

I don't see the problem then. While I never heard about vectorization, this is basically an identification (one of many) that allows us to give matrices topology that from R^{mn}

Its identification of the two as sets which we make into homeomorphism

ok

But maybe you have topology given by e.g. operator norm and you need to show its the same as product topology

Depends on your definition

This would go under all norms on R^n are equivalent

that is, you could say that the Euclidean norm coming from this "vectorization" is a norm equivalent to the operator norm

and it should be well known that $\mathbb{R}^n$ with Euclidean norm has topology that of product topology

@SoumikMukherjee Gg :)

Morning

hi

Also I got a research cs job and will be starting on the 17th

cool

I made a coffee in a moka pot

@SineoftheTime ty:)

Rip tried to get a second remote job but looks like it's going to be a rejection :'(

Oh I didn't even realize EE18 was responding to me

I've deleted the whole conversation 4-8 am from my mind

@EE18 I'd say this is not something that one should generally expect someone to find, apart from maybe some specific examples. Don't worry about it

@EE18 by tidy up presumably you mean reparametrizing, sure.

@EE18 the first inequality comes from $r_{n_1} > r_{n_2}-1/N$ and $s_{n_1} < s_{n_2} + 1/N$, both follows from the preceeding two inequalities

@Jakobian What nonsense.

Mandelbrot set therefore Christian God. This can't be nonsense, just because the argument whatever it is could be replicated for every possible religion in the world if true.

What a nonsense ! Mandelbrot-sets to prove the Christian god. "Atheists nightmare" - LOL

As far as I know , we do not have the first April. So, the date to post this is the wrong one.

Hi

@ShaVuklia Glad we could help.

I don't understand why same limit, different result

wolfram tells me 0, mathdf tells me -8

does anyone know why?

@Pizza I'm too lazy to work through the limit myself, but an obvious place to start is with the definition of $\log$---is it the same as the natural logarithm, nor not?

@XanderHenderson wolfram translates ln to log automatically, same thing mathdf translates log to ln

If you say so.

yes you can also check it yourself

this is the error

wolframalpha.com/…

they failed at Taylor polynomial of $\ln(8x^2+4x+1)$

$\ln(8x^2+4x+1) = 4x + o(x^2)$

wolfram is correct, mathdf isn't

ah yes, exactly, thanks @Jakobian

Assume $X,Y$ are nice compact metric spaces. Assume $F:X\times Y\to \mathbb{R}$ is continuous and $U$ open in $X\times Y$ and $C$ is compact in $U$. Suppose $F|C=0$ and $F=1$ away from a closed et $K$ containing $C$ in its interior. To show this, why does it suffice to show it for product $U$ and product $C$?

monoidal: to show what? the existence of such F, given U and C?

I dont know what the question is but the answer is most surely because you can find a partition of unity living on sets taht are products

@leslietownes I mean why to show it holds for arbitrary U and C, it suffices to show for product U and C? @leslietownes @s.harp

@XanderHenderson quack

monoidal: yeah, but what is the "it" in "it holds"? you have an "assume" about an F and a "suppose" about the F, as if you're setting the stage for some other statement about F that will be the thing you are thinking about proving.

Sorry what I want to show is if it is true, why would it suffice to show for product U and C

what is the "it" in "it is true"? that, given U and C as stated, a continuous F can be found satisfying those conditions?

yup @leslietownes

you're assuming the spaces are nice anyway, so this holds irrespective of worrying about products

it's just Urysohn's lemma

yes, but im interested in the product method

join into the discussion here

well, it's interesting to i guess reverse engineer a more interesting exercise out of this. does a product of two spaces that satisfy urysohn's lemma also satisfy urysohn's lemma? if not, what about a product of two compact spaces that do?

once you assume these things are metric spaces, are you not just proving/assuming urysohn's lemma for metric spaces (which the product of two metric spaces would be)?

@Peter All of their 13 answers are about order of operations 💀

@SoumikMukherjee The user continues to claim the false statement , maybe more users disagreeing finally convinces him/her.

How can I calculate , say , $(18!)!$ modulo a prime number larger than $18!$ , in other words , how can I apply trial division to something like $(18!)!+1$ ?

@leslietownes the question becomes is product of two normal spaces normal

and this is actually very hard question

and the answer is no

I mean maybe not hard, but it opens some can of worms

yeah, so I maintain that monoidal should just appeal to Urysohn's lemma

what I want to know is what the product method is

> To show this, why does it suffice to show it for product U and product C?

this needs some context imo

@Thorgott I want to ask, if I ever wanted to learn algebraic topology, would you recommend any texts for it?

@Jakobian Hatcher is a pretty standard recommendation. You'll either love it or hate it.

It has the advantage of being freely published on the author's website, and is otherwise quite cheap for a mathematics text.

I'm not Hatcher's audience

i.e. I will never read it

i am definitely in the 'hate it' camp, although i took some classes that used a lot of it and probably learned more from it than from other sources

There is also Bredon's book, which I think can be legally downloaded for free (it is the the yellow Springer series, but I think that the author makes it available).

I am less familiar with that one, having skipped around it a bit---for me, it is more of a reference than a book that I learned out of.

> The golden age of mathematics-that was not the age of Euclid, it is ours.

@Jakobian is there anything specific you would want to learn?

nothing specific

I never really lliked Hatcher's book, but the impression I get from his wevsite is that he is a pretty cool guy

reading Bredon's book is probably my best option

Bott & Tu is also fantastic

it even has spectral sequences in the middle

my general go-to recommendation is Hatcher, but Bredon is one of my favorite books

it's a lot more challenging, but I don't think that'd be an issue for you

it has some more geometric sections, which may or may not appeal to you

if you want something with a more homotopy-theoretic tint, then tom Dieck is also an excellent book

I have tom Dieck fully printed, but since that theorem I read that needed correction I had mixed feelings about reading it

Okay, I'm used to seeing proofs of the Riemann Hypothesis, counterexamples to Collatz, miraculous twin primes, and Cantor denial on Math SE. But order of operations dogmatism is a brand new one on me.

> He is wrong. Maths is never ambiguous.

Mathematics is done by people which can be ambiguous in what they mean.

"Maths" may never be ambiguous (whoever they are), but human beings are more than capable of writing things in an ambiguous manner.

> if you want to know the current state of affairs then pick up a Maths textbook.

#>:(

@s.harp Appeal to authority. Yay.

Note that there are many similar answers.

I was employed at a dual university (for engineers) for a time. The attitude of answerer regarding the rigidity/correctness of conventions was something I saw for the first time in that setting, it was slightly disorienting to see people argue about things I thought to be irrelevant

@Jakobian which one?

@Thorgott exponential law for based spaces

I probably mentioned it few times here

it just gave me off a vibe that the author doesn't really care about the statements of their own theorems

what a ridiculous thing to say