/mg/ math general

[Anonymous No.10042555]

/mg/ math general

For your stupid questions, go ask /sqt/.
For your homework, go ask /sqt/ or
>>>/wsr/

Previous thread >>10026711


no memes edition

[Anonymous No.10042609]

>>10042555
first for asking for an introduction to the long standing inside jokes/common posters on this general.
also, I'm betting 6 (you)s on a future fields medalist having been on here.

[Anonymous No.10042617]

How the hell do I do an e-d proof for a function that’s the reciprocal of a polynomial? Seriously about to kill my self. This is the one problem preventing me from going to sleep. I found my del but manipulating the function to become an epsilon is retarded

[Anonymous No.10042624]

>>10042555
lol that fucking gif

[Anonymous No.10042627]

>>10042617
look at the new /sqt/ OP post, then also at the new /mg/ OP post

[Anonymous No.10042651]

>>10042627
I’m not posting with the calc 1 brainlets sorry. This has to do with proofs and questions about proofs never even get answered there.

[Anonymous No.10042665]

>>10042651
i answer every single shit tier analysis question, calculus, algebra, etc there, so you're pulling that shit out of your ass. And the fact that you think you're somehow superior to calc 1 baby is honestly hilarious

[Anonymous No.10042667]

>>10042616
>I have no clue what's in the forefront desu
To be honest, neither do I, but I do remember seeing a set of books on the subject that were nice
>>10042609
>first for asking for an introduction to the long standing inside jokes/common posters on this general.
Are you referring to 2hu, the gorilla poster, and the ones from vixra?
>also, I'm betting 6 (you)s on a future fields medalist having been on here.
Wouldn't that be amazing. I can't say I wouldn't like to be one.

[Anonymous No.10042670]

>>10042555
Can someone clarify the topology of CW complexes for me?

Hatcher defines it as the weak (initial) topology with respect to the characteristic maps of all the cells. nLab defines it as the strong (final) topology with respect the inclusions of all the n-skeletons. Are these the same or is one of them wrong?

[Anonymous No.10042671]

>>10042667
>but I do remember seeing a set of books on the subject that were nice
They were by Silverman, I read his number theory book and it seems he has other, more advanced texts, just found one
http://www.pdmi.ras.ru/~lowdimma/BSD/Silverman-Arithmetic_of_EC.pdf

[Anonymous No.10042689]

>>10042670
they're the same. They're just defined in opposite directions (that is, in one you "build" the complex from the ground up, and in the other, you "deconstruct" it)

[Anonymous No.10042760]

>>10042667
yeah, some links or a summary to their personas would be great.

[Anonymous No.10042896]

>>10042760
I don't really think anyone is autistic enough to actually write summaries elsewhere about them but I can tell you a bit of what I remember. The gorilla poster was frequently banned and usually asked either pretty basic or would suggest really strange things. The people from vixra and the people who pretend to be them are also frequently banned but usually come back in some form to post about their theory of everything or the riemann hypothesis. Among all the people I've mentioned the only one who seems to actually be knowledgeable of mathematics is 2hu, basically this guy who posted about mathematics related to theoretical physics. He used to type up a whole bunch of latex and then post it here concerning his work or ideas. Not sure if he actually posts here anymore or if it's one of the many copycats. Other than that there's the usual shit posters that come in different varieties and some guys who just like posting about math and what not.

[Anonymous No.10043208]

Alright lads, masters in CS or applied math?

[Anonymous No.10043212]

>>10043208
>CS or applied math
Applied math, then learn any relevant CS on the side. Hell, there's a lot of pure mathematics that's being applied to CS nowadays so you can't go wrong given the right fields.

[Anonymous No.10043218]

>>10043208
One gives you a good job, the other one forces you to live under bridges. I'll let you figure out which is which.

[Anonymous No.10043220]

Is pic related good for people who struggle with math?

[Anonymous No.10043227]

>>10043218
>>10043212
Applied math it is then, thanks lads.

[Anonymous No.10043248]

>>10042609
>a future fields medalist
C'est moi.

[Anonymous No.10043262]

show of hands if you're okay with this video guys

[Anonymous No.10043263]

>>10039620
I seem to be highly resistant to most psychoactive substances. It's something that makes me seriously consider reincarnation as a possibility. I think I did a lot of drugs in my previous life and my new self inherited the built-up tolerance to them.

[Anonymous No.10043265]

>>10043262
Haven't even watched it. Don't plan to either.

[Anonymous No.10043275]

>>10042651
Lol,i learned epsilon Delta on calc 1and I'm from a shithole country, where are you from boi?

[Anonymous No.10043292]

How do I get into a good grad school?
t. college freshman

[Anonymous No.10043309]

>>10043292
work hard, achieve top grades, attempt putnam or whatever competition you can, ask your lecturers about research you can do now or during the summer, excel at your thesis, take as many graduate courses as you can without getting bad grades.

That's about it

[Anonymous No.10043311]

>>10043292
Start taking proof based math courses asap and continue on from there. The main reason I say this is so you can start working with a prof to do some research, maybe even get a paper or two under your belt (that'd really help you out). Getting mostly A's in your math coursework, taking a couple grad courses, getting a decent math gre score, and some strong letters of rec will basically get you into most grad school. Having volunteer work and being an officer in some organization will help as well.

[Anonymous No.10043338]

>>10043220
Can someone answer my question?

[Anonymous No.10043346]

>>10043220
>Is pic related good for people who struggle with math?
Why don't you read it and find out?

[Anonymous No.10043348]

>>10043338
How would anyone here even know if that book iis any good? Hello? Think.

[Anonymous No.10043547]

>>10043220
I haven't read it but I have seen the associated material and some of her talks. They seem fairly standard, you may learn a few new tricks that may be useful for you. For me the thing that always helped me gain new perspectives on mathematics was just reading essays by other mathematicians. If you've read any bit of James Newman's world of mathematics of checked our the Princeton companion to mathematics you'll know what I mean. That book will probably at least be somewhat useful and not a waste of time.

[Anonymous No.10043738]

>I learn math for fun

[Anonymous No.10043751]

>>10043738
>I learn math for fun
W-what's wrong with that?

[Anonymous No.10043763]

>>10042896
Yukarifag was the smart one

Ranfag is just a shitposter

[Anonymous No.10043787]

>>10043763
they are the same individual likely having a split personality disorder

[Anonymous No.10043793]

>>10043751
Nothing. Good on you.

[Anonymous No.10043826]

>>10043787
Nice try Ranfag, we know you aren't him.

[Anonymous No.10043976]

>>10043826
I'm morbidly curious, do you have any evidence to support that statement?

[Anonymous No.10044185]

>tfw constantly oscillate between thinking I want to devote myself to maths for the rest of my life and thinking I should just get a part-time codemonkey job and spend my free time going /out/
Help

[Anonymous No.10044243]

>>10044185
>selling out for money
I would anhero instead

[Anonymous No.10044280]

>>10044243
Rather than selling out, it’s accepting that you don’t want to spend your entire life being a below average mathematician.

[Anonymous No.10044295]

>>10044243
I don’t want money, I want the means to pursue my interests. My turmoil is over whether my love for mathematics trumps all my other loves.

Also >>10044280
is also a factor, seems like a fucking nightmare getting into acedmia these days.

[Anonymous No.10044363]

>>10043763
>Yukarifag was the smart one
lol, he was a retard. Most of "his" posts were either pure gibberish or trivial "it follows from the definitions" puke.

[Anonymous No.10044364]

>>10044363
>was
"He" *is* a retarded shitposter still. Just lazier nowadays.

[Anonymous No.10044366]

>>10044185
It won't work dude. For some reason CS people are very wary of math grads in coding. Every interview I had was extremely hostile. They seems to think mathfags are too systematic and are unable to adapt properly to the task or adjust our workflow to shifting goals.
When they don't do that they complain that you're overqualified.

Fuck this shit.

[Anonymous No.10044399]

>>10044366
I already have a CS job though

[Anonymous No.10044451]

>>10044399
How'd you do it? I have been trying for a month to no avail.

[Anonymous No.10044474]

>>10042896
>The gorilla poster was frequently banned and usually asked either pretty basic or would suggest really strange things.
Only frequently banned because of fascist alt-right mods, and we don't know what you mean by "strange things".

[Anonymous No.10044526]

>>10043220
coincidentally I'm reading it right now but am just on the beginning (10%). It gave some interesting facts but nothing very practical yet. Why don't you download the pdf and skim through it? It won't take much time and you definitely can get something worthy out of it.

[Anonymous No.10044858]

How do you guys balance reading thoroughly and reading speedily? I do a very thorough first reading of the material, but it's time consuming and I'm always lagging behind the lectures.

[Anonymous No.10044860]

>>10044858
You need to accept that you won't understand material 100% all of the time. I try to get enough understanding that I have intuition for why things work / are the way they are. Then over time I can come back and drill down the actual proofs for things.

[Anonymous No.10044907]

>>10044858
you are doing the opposite. You are supposed to skim through the whole text (be that a book, section or specific chapter) so that you get a picture of the whole, where the text is going, what it is about, what is the point of it. After that you read focusing and dedicating the needed time on what is really relevant.
If there are exercises/questions at the end of the text it is even better, you read the questions first and read the text afterwards with the questions in mind.
>source?
any book on methods for better reading/understanding/memorizing texts, such as Adler's 'How to Read Books' or even >>10043220 this one.

[Anonymous No.10044982]

>>10044295
>My turmoil is over whether my love for mathematics trumps all my other loves.
>>10044185
>I should just get a part-time codemonkey job and spend my free time going /out/
>Help
I've mentioned before in /mg/ and I've posted links but I can post some more, there's a ton of mathematics becoming more and more applicable to CS, so not only can you do mathematics, but you can do it a much higher level and sophistication than your CS counterpart can. Academia isn't the only way to do research per se. Microsoft, for instance, hires mathematicians to work under them. I think Micheal actually works as a mathematician under them. You could also do what a lot of other people do and be a mathematician but work in a different department. That's basically what mathematical physicists do. Do that in CS if you think working in math department is too difficult. I'm just saying, math is a wide field and can be applied to a whole range of topics, don't think you can't apply it to another field you enjoy, without reason of course. Also plenty of math people spend time getting /out/, one of them unfortunately died though.
>>10044907
I'll second any of Adler's "How to" books, I was surprised it wasn't standard reading in my college, or high school for that matter.

[Anonymous No.10044990]

>>10044858
>>10044907
>>10044982
Since I brought it up and you replied, here is a quick rundown of Adler's How to Read a Book.

[Anonymous No.10045005]

>>10044982
Can you get an industry mathematics research job without being in something applied and having an advanced degree though? Like right now I just have an undergrad + honors thesis in algebra (well a subfield but I don't want to dox myself), I doubt I'm very useful. My strongest skill is probably deep familiarity with linear algebra desu. I mean I can program and shit too but so can all the cs kids.

[Anonymous No.10045024]

>>10044982
>>10045005
And it's not so much the choice of working in mathematics or not that's bothering me, it's the idea that I may be able to live a comfortable life with lots of leisure time for my other interests by say, freelancing 25 hours a week. It sounds appealing, but I don't know if I'd be happy having given up maths.

[Anonymous No.10045095]

>>10044860
It's a good point, that is hard for me to accept. The only reason I made it into real math was by not moving on in proofs until I understood every step, and then could reproduce the proof with full justification. But I agree I should accept that I won't master the material right away now that I'm past that transition stage.

>>10044982
>>10044907
>>10044990
This looks like it's for how to understand books in humanities desu. I'm doing 3rd year topology and abstract algebra atm. Not sure how well this would apply.

[Anonymous No.10045113]

>>10042555
Is there a script to download not only the paper but also all the referenced paper form arxiv?

[Anonymous No.10045119]

>>10045113
Wouldn't that just end up downloading the whole archive or would it stop after one level?

[Anonymous No.10045126]

How do people cite old results in their papers? Like say I want to reference Cayley's theorem, do I need to dig up an old paper from the 19th century or can I assume everyone knows what I'm talking about.

I imagine you'd still need a citation if it was a more obscure result though, so how would you do that? Does like the French academy keep those papers or something?

[Anonymous No.10045130]

>>10045126
By "old" I mean 100+ years ago, if that wasn't clear

[Anonymous No.10045140]

>>10045119
I would be happy with 1 level

[Anonymous No.10045176]

>>10045126
>it is well known that...

[Anonymous No.10045258]

>>10045126
Usually you can cite reference books and what not. Some books act as compendiums for a large amount of commonly cited theorems and results, making it kind of a one stop shop. Just cite a textbook that contains the result and you'll be fine.
>>10045095
>This looks like it's for how to understand books in humanities desu.
They act as general guides, you can usually modify them depending on the subject. It is worth mentioning that in Adler's book he has specific sections for things like scientific papers. In any case I do think some of the methods are useful. reading the text once through gives you a rough idea of where things are going which can be nice. Not the entire book just a section at a time. Note taking methods are always useful, same with getting a organization that's suitable for you. As for the comparisons, it is worth mentioning that few books contain all the relevant material for a field, even for introductions. Hell, people introduce entire fields in different ways. Compare the styles of analysis between a text like Rudin or Pugh or Tao. People approach topics in different ways and come from different motivations, so you can compare them. Tao has a nice article about this, something called "learn, then relearn your field"

[Anonymous No.10045261]

>>10045005
>>10045024
>Can you get an industry mathematics research job without being in something applied and having an advanced degree though?
I'd say it depends on the person but usually a master's degree or a solid undergrad degree works well. I guess it depends on what kind of math you like and what fields of CS you want to work in. I can understand wanting a lot of downtime. One option is becoming an amateur mathematician and working in combinatorics or number theory. It's not uncommon, I'd just make sure not to turn into a crank.

[Anonymous No.10045313]

>>10045176
>see [work not publicly available]
This in particular was pretty annoying when I started doing research. In my field there are quite a few very often-used results proved in certain theses which were never published anywhere so you have to contact the professor themself (or find somebody else who has it) if you want a copy of them.

[Anonymous No.10045325]

>>10045313
>In my field there are quite a few very often-used results proved in certain theses which were never published anywhere so you have to contact the professor themself
It gets worse when it's not even in a thesis but just unpublished and in the folklore, like someone mentioned it in a conference and nowhere else. Or they claim the result in a follow up paper that never gets publish, looking at you Gromov.

[Anonymous No.10045981]

>>10045258
Fair enough, as something to mould to the task at hand I can see it being useful. Skimming the upcoming sections is something my prof did recommend, and in general the techniques would help with getting a gestalt view of things. Sometimes in math I lose the forest for the trees and have thought I should work on cultivating a "zoomed out" perspective on the material a bit more. I'll have a read of that article as well.

[Anonymous No.10046003]

>>10043738
same
studying math for me

[Anonymous No.10046091]

Given a point on a regular polygon, is it true that there is a non-trivial symmetry that leaves it unchanged? Why?

(trying to prove that the stabilizer of every vertex under the group action of the symmetries acting on the vertices has two elements)

[Anonymous No.10046105]

>>10046091
I don't know why you would be considering arbitrary points on the polygon when you are considering the action on the vertices. It's not true, anyway. Most points on the interior of an edge aren't fixed by anything.

Just use the orbit-stabilizer theorem.

[Anonymous No.10046107]

>>10046091
>Given a point on a regular polygon, is it true that there is a non-trivial symmetry that leaves it unchanged?
What have you tried?

[Anonymous No.10046200]

>>10046105
>>10046107
I'm retarded. That's about it. :(
Why can I make long abstract proofs but someone asks me to apply what I know to other subjects and I immediately explode? Is that a symptom of autism?

[Anonymous No.10046335]

>>10042896
Hi.
I'm trying to get a paper published soon and I got a bf, so I don't spend nearly as much time on 4chan as I used to, though I still browse through once in a while. Just a heads up.

[Anonymous No.10046340]

>>10046335
gay detected, lol

[Anonymous No.10046373]

>>10042555
hey mathletes, I need your advice, I have a bsc in chemistry (pchem) and I am interested in doing a msc project in quantum chem or spectroscopy, both which are math heavy.

I wanna get better at math, I'm rather proficient, but I wanna have that intuition you mathfags have, recommend me a book? calc/linear algebra that sorta thing

[Anonymous No.10046494]

Anyone built a successful career?

[Anonymous No.10046532]

>>10046494
Do careers even exist anymore? From my experience larp'ing abroad in euroland it seems most educated professionals constantly move between jobs, and america seems like its moving to a similar system.

[Anonymous No.10046903]

>>10046335
What are you doing here?
you have no power here back to >>>/jp/

[Anonymous No.10046937]

>>10046532
The non-pleb echelons of the business world more or less function like you say. People generally don't stay in one place very long. You can stay in grunt-level careers for longer, but even in shitty McDicks-tier jobs they will try to push you up the ladder eventually.

Academic careers do still exist, although the norm nowadays is bouncing around a few postdocs first unless you had an extraordinarily productive PhD or you got it from Princeton or something.

[Anonymous No.10046940]

>>10046494
>Anyone built a successful career?
oh you

[Anonymous No.10047522]

>>10046532
Jumping from a job to another is fine as soon as their a clear perceptive like in the US.

In some europoor countries like Germany, there is even a law that forbids you to work in academia more than 6 yrs.

I'd be happy to change jobs if they were permanent. At least I'd have security with the current job each time.

As for now, it is a pathetic survival horror. That's what it is

[Anonymous No.10048427]

https://arxiv.org/pdf/1810.02204.pdf
>A simple derivation of the Riemann hypothesis from supersymmetry
>Ashok Das, Pushpa Kalauni
>(Submitted on 3 Oct 2018)
>We give a proof of the Riemann hypothesis based on ideas from supersymmetric quantum mechanics.

[Anonymous No.10048454]

>>10048427
>supersymmetry
dropped

[Anonymous No.10048476]

>>10048427
What's up with all of these physicists that think they know number theory?

[Anonymous No.10048490]

>>10048427
Why do quacks like two-column formatting so much?

[BigGuy !pZ5bp8ocMc No.10048526]

>>10043263
Weirdly enough I feel deja vu reading this

[Anonymous No.10048543]

>>10048427
>Physics
*sneeze*
I’m sorry, I’m allergic to bullshit.

[Anonymous No.10048562]

Is this accurate?

[Anonymous No.10048567]

>>10048562
absolutely

[Anonymous No.10048581]

>>10048567
Would you mind showing me your character sort buddy?

[Anonymous No.10048634]

>>10048581

[Anonymous No.10048782]

>>10048427
>GM
Lol. It was shown last year that there's a Hamiltonian whose eigenvalues reproduce the zeros of the zeta function but the well-posedness of its eigenproblem hasn't been demonstrated untl now. Do these pajeets think they're breaking new grounds or something?

[Anonymous No.10048793]

>>10048562
Yes, geometryfags are a bunch of queers.

Lol, geometry...

[Anonymous No.10048804]

>>10048562
swap applied for water dog, all the normies go for water dog. umbreon is for autistics, like actuarial work.

[Anonymous No.10048826]

>>10048793
>muh topology elegant le approach el watch me deformed creatura both mathematica and irl

[Anonymous No.10048896]

Friendly reminder that geometry is the oldest math branch ever

[Anonymous No.10048901]

>>10048896
based and redpilled

[Anonymous No.10048902]

>>10048896
based and honest

[Anonymous No.10049048]

>>10048804
Actuarial at my uni is what all the girls and frat kids do

[Anonymous No.10049066]

what math do I even like?
iI don't like geometry and I hate word problems yet I also find pure maths somewhat boring I am also somewhat retarded at math but I want to get into it

[Anonymous No.10049068]

>>10048427
Cringe.

[Anonymous No.10049074]

What do people mean when they say "geometry" in the context of modern mathematics? They're talking about algebraic geometry and shit right?

[Anonymous No.10049087]

>>10049066
Maybe you don't like it buddy. I mean, don't expect to be an easy path were you can just investigaye whatever the hell you want. Even in math you are going to spend a great deal doing bullshit work.
>>10049074
Geometry is one of the most extensive fields of mathematics and so it's a bunch of shit. What I belive that modern mathematicians refer to when describing something as geometric, is more about the tools you use to attack a problem or how you define it. For example ODEs can be thought, purely with analysis as relationship between functions and their derivatives, but you can also look it as vector fields and integral curves.

[Anonymous No.10049105]

>>10049074
differential geometry. algebraic geometry is of course an extensive field but "it's not really geometry" if you ask me.

[Anonymous No.10049127]

I'm dumb

[Anonymous No.10049190]

Can some explain this to me?

1st picture

[Anonymous No.10049192]

>>10049190
second picture

[Anonymous No.10049196]

>>10049192
and third picture

so the idea is, you get from 2 to 3 by using 1. I don't get the maths.

[Anonymous No.10049203]

>>10049196
sorry, you get 3 from 1 by using 2***

[Anonymous No.10049224]

halp

[Anonymous No.10049225]

>>10048543
nature's logic is better than human logic tho

[Anonymous No.10049230]

>>10049224
What is delta?

[Anonymous No.10049264]

>>10049230
dirac delta :s

[Anonymous No.10049341]

>>10049264
that integral equals 1 following the Dirac delta definition my dude

[Anonymous No.10049345]

>>10049341
i don't know how

and then if it was from a to 2a, would that also be 1, or why would it not be?

[Anonymous No.10049347]

>>10049345
it's hard to tell cause that's not in a function properly speaking, I'm not an expert on the topic

[Anonymous No.10049352]

>>10049347
ok, thanks for the help anyway

[Anonymous No.10049355]

>>10049190
>>10049192
>>10049196
>>10049203
ϕ1 is piecewise-linear with 4 regions. ϕ* has 5 regions based upon which regions of ϕ1 are within the integration range (1, 1-2, 2-3, 3-4, 4). Both ϕ1 and ϕ* are symmetric about r=0, so the 4 cases for ϕ1 can be expressed as 2 cases using |r|, and the 5 for ϕ* as 3 cases using |r|.

The outermost case is just an integral where ϕ1=0 over the integration range => ϕ*=0. The second case has ϕ1=0 for part of the range and ϕ1=1-|r'| for the other part, with the integration limits depending on r:
[eqn]\int_{-1}^{r+0.5}\ 1+r'\ dr'[/eqn]
[eqn]\int_{r-0.5}^{1}\ 1-r'\ dr'[/eqn]
The innermost case has regions with ϕ1=1+r' for r'<0 and ϕ1=1-r' for r'>0.
[eqn]\int_{r-0.5}^{0}\ 1+r'\ dr' + \int_{0}^{r+0.5}\ 1-r'\ dr'[/eqn]

[Anonymous No.10049367]

What's a computationally efficient way to check if a matrix is invertible?
Computing its determinant is too expensive

[Anonymous No.10049369]

>>10049355
that's sick, I'm just trying to find how to activate math mode now lol

[Anonymous No.10049377]

Any help on this: >>10049368 ?

[Anonymous No.10049381]

How much math does the average normie know?

[Anonymous No.10049489]

>>10049381
I think it is safe to say that the average normie has a firm grasp on arithmetic and nothing else.

[Anonymous No.10049543]

>>10049203
What do you not get exactly? Simply calculate the integral. The easiest to see is for 0; when we plug in the borders, the lower is r' = r-0.5 and we know it's 0 when |r'|>1, which is when |r| > 1.5 etc

[Anonymous No.10049569]

>>10049489
Not even that. I daily see people use a calculator for things like 12*6

[Anonymous No.10049572]

how do you read math mode?

[Anonymous No.10049577]

>>10049569
Well, that just means they are lazy but if they are calculating 12*6 it is fair to say that at least they understand what arithmetic means.

[Anonymous No.10049599]

>>10049367
>O(n^3) is too expensive
Stop using a potato-powered calculator

[Anonymous No.10049603]

>>10049599
Well, it's quite expensive a check if I want to know whether or not I can call a matrix inverse subroutine.

[Anonymous No.10049889]

What advice do you have for turning math education into a hobby? I enjoy calculus, but it feels shallow learning to do one type of problem in class and moving on to the next without any kind of theoretical understanding or real-world application of the material we pick up. That would benefit my learning a lot, yet I'm not sure how to implement it. I guess in the meantime I'll skim through my textbook looking for topics that catch my eye, but any advice would be appreciated.

[Anonymous No.10049950]

>tfw find arithmetic proofs hard as fuck
Am I a literal retard? I've been spending an hour on trying to prove that (a - b) could divide (a^n - b^n) within Z (with n being a nonzero natural number)
I'm just moving from exercise to exercise and there are none I'm capable of doing.

[Anonymous No.10049973]

>>10049572
adblock off

[Anonymous No.10049979]

>>10049950
This is a trivial inductive proof. Under which assumptions are you working? Stuff like this is as easy as it gets, the only reason it should require any work at all is if you have to define operations on [math]\mathbb{Z}[/math], and even then it's just a few minutes.

[Anonymous No.10049989]

>>10049979
Huh? What is your inductive step? Just factor out the (a - b) desu, far simpler.

[Anonymous No.10050017]

>>10049979
I didn't think about using a proof by induction. I did as >>10049989 said originally but I arrive at a^n - b^n = (a - b)(a^n-1 + b^n-1) + ba^n-1 - ab^n-1 which doesn't help.
There's also "prove that 3 divides (2^n - 1) within Z, with n being an even natural number" and "determine the remainder of the euclidean division of (n^3 - 2) by (n - 2)"
I don't know if I'm too tired or something but every single one of those is giving me trouble even though I'm aware that they shouldn't

[Anonymous No.10050038]

>>10050017
If you've got a^n - b^n = (a - b)(a^n-1 + b^n-1) + ba^n-1 - ab^n-1 you've shown that (a - b) divides a^n - b^n though?

>prove that 3 divides (2^n - 1)
Work modularly

>determine the remainder of the euclidean division of (n^3 - 2) by (n - 2)
That's just an algorithm, which, admittedly, can be weird to apply to polynomials if you weren't taught long division well.

[Anonymous No.10050048]

>>10050038
>you've shown that (a - b) divides a^n - b^n though?
I always manage to miss the most obvious shit when it's right in front of me. Thanks.
>modularly
You mean by applying divisibility rules within Z/congruence relations? I don't do math in english sorry
>That's just an algorithm
What algorithm are you referring to?

[Anonymous No.10050056]

>>10050048
>You mean by applying divisibility rules within Z/congruence relations? I don't do math in english sorry
Yes congruence relations. Specifically Z/3

>What algorithm are you referring to?
The Euclidean algorithm

[Anonymous No.10050059]

>>10050056
Thanks again. I hope my problem-solving will get better with practice because I'm kind of worried now.

[Anonymous No.10050637]

I sure hope majoring in math works out.

[Anonymous No.10050642]

>>10050637
You'll be fine. The service industry is always in need of workers.

[Anonymous No.10050645]

>>10045113
Write one yourself

[Anonymous No.10050650]

>>10050637
If it doesn't, just switch to CS.

[Anonymous No.10050710]

>>10050650
Yeah I'm double majoring in CS as a backup plan.

[Anonymous No.10050737]

>>10049367
> Computing its determinant is too expensive
Aside from expense, if you're dealing with floating-point values then matrices are almost always invertible in the sense that their determinant isn't exactly equal to zero. But calculating their inverse will result in a matrix whose entries are essentially rounding errors.

Realistically, you either accept that you're going to get garbage when a matrix turns out to have near-zero determinant, or you calculate error bounds and check whether the bounds include zero.

[Anonymous No.10050825]

i fucking hate this general

[Anonymous No.10050925]

>>10050737
I mean do I have to compute the determinant to check whether it makes sense computing the inverse or is there some kind of trickery i can use instead?

[Anonymous No.10051052]

No one answered in /sqt/ so:
How do you compute the odds of winning in "system" lottey picks?
I.e. assuming a 6/58 lottery, instead of picking 6 numbers, you can do "system 7", picking 7 numbers instead and you can use any 6-combination of the 7 numbers to match to the winning lottery numbers.

t. Cpa/cfa math brainlet

[Anonymous No.10051385]

>>10050825
Don't steal my meme faggot: -I- hate this general. I really, truly do.

[Anonymous No.10051438]

What's a good intro to Lie groups? Do I need to know differential geometry first?

[Anonymous No.10051483]

Does anyone here study at Bonn? Maybe even met Scholze? How does he smell like?

[Anonymous No.10051504]

Help a brainlet out, what are the representations of the circle group? I think they should be rotations by multiples of 2π (which makes the duality with Z obvious), but aren't any two such functions identical if you drill down to the formal definition of a map?

[Anonymous No.10052126]

>>10051504
If I have to ask rebbit I swear to god

[Anonymous No.10052150]

>>10051385
Then why come here?
>>10051438
>What's a good intro to Lie groups? Do I need to know differential geometry first?
Well Lie groups are smooth manifolds, so yeah, some differential geometry would be good. How in depth do you want to go? Lee's book on manifolds goes into lie groups but only really covering the basics.
>>10051504
>but aren't any two such functions identical if you drill down to the formal definition of a map?
Mind explaining what you mean? Yeah, the representations of the circle group are [math]e^{2\pi in\theta}[/math] and they are not equivalent to each other, in fact they're orthogonal, which is easy to see when you remember they form the fourier series, at least if I'm remembering right, it's been a while, let me check some other sources.

[Anonymous No.10052247]

>>10052150
>Mind explaining what you mean?
[math]e^{2\pi in\theta} = e^{i\theta}[/math], right? Which would make all characters the identity. That's clearly not right but I don't know why.

[Anonymous No.10052257]

>>10052247
Is it because the complex exponential branches? My complex analysis course wasn't very good desu.

[Anonymous No.10052320]

who's your favourite martian composer?


.... please help

[Anonymous No.10052333]

>>10043212
Which pure math fields are being applied to cs?

[Anonymous No.10052340]

so what would be the better degree to do if i wanted to get into AI? joint mathematics and computer science or computing (with artificial intelligence and machine learning)? bearing in mind the ai and ml aspect doesn't begin until the third year, until then it's just a cs degree, and i can take ai and ml modules in jmc anyway.

[Anonymous No.10052360]

Anyone here teach math at a college or uni? any thoughts on it?

[Anonymous No.10052414]

>>10052333
Algebraic topology, Algebraic geometry, Number theory, Category theory, Differential geometry.
>>10052247
A good rule of thumb is to just plug in a few numbers and check
Let's choose something random like n=2 and [math]\theta=\pi/2[/math] and let's assume you're correct, then
[math]-1=e^{i\pi}=e^{2i\theta}=e^{i\theta}=e^{i\pi/2}=i[/math]
But that's clearly wrong. I think what's happening is that you're assuming something to the effect that
[math]e^{(n+1)i\theta}=e^{ni\theta}e^{i\theta}=e^{i\theta}[/math]
But that's not true at all, reminder that
[math]e^{ni\theta}=1[/math] only for the root of unity.

[Anonymous No.10052432]

>>10052414
>root of unity.
roots of unity
>>10052320
xy is a song, since it starts with x, ends with y and contains two copies of an existing song, namely no notes. Therefore, by rule 3, so is yx. Now apply rule 2 again and we get x(xy)(xy)y and x(yx)(yx)y. That's two songs of length 6. To get two more just apply rule 3 to get y(yx)(yx)x and y(xy)(xy)x. Are you starting to see the pattern and how this generalizes?

[Anonymous No.10052441]

>>10052432
i get it now i just didn't understand what rule 3 meant initially

[Anonymous No.10052449]

>>10042555
What is the complexity of rank matrix factorisation, ie given A finding B, C such than A=B*C and inner dimension of B and C is rank(A)?
Or at least in particular case when rank(A) = 1.

[Anonymous No.10052521]

>>10052247
>[math]e^{2\pi in\theta} = e^{i\theta}[/math]
LMAO

[Anonymous No.10052585]

>>10052414
Yes you're right, I'm dumb

>>10052521
I mixed up my multiplication and addition it's confusing when you're doing representations no bully

[Anonymous No.10052962]

am i a brainlet

[Anonymous No.10053015]

i remember a video about a math teacher drawing really nice lines and circles on blackboard quickly and precilsely. Do you perhaps know about it?

[Anonymous No.10053468]

>[math]\frac{\partial}{\partial t}[/math]

[Anonymous No.10053878]

What are you reading?

[Anonymous No.10053943]

>>10053878
Book of Psalms. Super boring.

[Anonymous No.10053951]

>>10053015
https://www.youtube.com/watch?v=raurl4s0pjU
is this what you mean?

[Anonymous No.10053956]

>>10053943
Ah yes, the Book of Psalms. My favorite passage in that book was when God said to David that he was God's begotten son.

Psalm 2:7
I will declare the decree: the LORD hath said unto me, Thou art my Son; this day have I begotten thee.

Seems like God has many sons, not just Jesus.

[Anonymous No.10053972]

Jumping from a job to another is fine as soon as their a clear perceptive like in the US.

In some europoor countries like Germany, there is even a law that forbids you to work in academia more than 6 yrs.

I'd be happy to change jobs if they were permanent. At least I'd have security with the current job each time.

As for now, it is a pathetic survival horror. That's what it is

[Anonymous No.10054096]

>>10050710
That's the best possible combination. It's perfect for quant funds.

[Anonymous No.10054312]

How can I find any two planes given the intersection line of the two planes, they give me this line:

x=1+t
L y=2-t
z=3-2t

[Anonymous No.10054340]

>>10052340
Math major is enough, CS minor if you want. ML/DL/NN are essentially stats.

[Anonymous No.10054348]

>>10052360
I was an adjunct for two years. What do you want to know?

[Anonymous No.10054349]

>>10054312
You need additional data

[Anonymous No.10054393]

What are best places in Europe to do a MSc and PhD in math? Are rankings to be trusted? Thank you

[Anonymous No.10054437]

>>10054393
If you are not in top 10 you wilk never make kid. Now I have to kill you.

[Anonymous No.10054825]

fucking anthropology students are apparent cases of dunning kruger
at my lowest i thought that dating one would be funny
turns out the autism chart for such individuals is incalculable
>likes mainstreamshit
>thinks that math is something impossible to approach
>speaks incoherently
>contradicts herself consistently, and is unaware of it which leads to me pointing it out
inb4 r9k
why the fuck are people so intimidated by fucking numbers?fucking enlighten me, because i'm infucking capable of understanding.
why seek argument about topics that you don't fucking understand?
i bolted when she stated that she was an ironic weeb, although indirectly.
this post is pure garbage, but i'm fucking drunk so i don't a give a shit.and fuck r9k

[Anonymous No.10054903]

>>10053951
Ahahah yea

[Anonymous No.10054909]

>>10054825
Its funnt that you considero average characteristics "autistic" in any sense.

[Anonymous No.10055001]

>>10054825
>her
There's your problem sweetie

[Anonymous No.10055121]

>>10054312
Given the general equation of two planes, Ax+By+Cz+D=0, Ex+Fy+Gz+H=0 that are not collinear, then you can find at least 2 of the coefficients given their line of intersection (or a relation rather). Then you can choose two random coefficients and calculate the other plane from it.

[Anonymous No.10055239]

Why are russian jews such good mathematicians? Fuck /pol/, theres no author like Arnold.

[Anonymous No.10055266]

>at a seminar
>relatively well-known old mathematician listening
>clear he knows he's 'too valuable' to be silenced or embarrassed
>always interrupts talks for minor details, or to say some rude comment
>everyone is always visibly annoyed
So I guess this is what my next 4 years is gonna be like...

[Anonymous No.10055273]

>>10055266
Give them a break. Deep in their hearts, every academic dreams of reaching that stage.

[Anonymous No.10055527]

>>10054312
The direction of the line is V=<1,-1,-2>, and the point P=<1,2,3> is on the line (and thus on any plane containing the line).

For any vector U which isn't a multiple of V, the cross product W=U×V is perpendicular to V (and thus to any plane containing the line). So the plane W.X=W.P contains the line.

Alternatively, if you want the plane defined by a parametric equation rather than an implicit equation, X=P+a*U+b*V.

[Anonymous No.10055661]

>>10055266
Was the talk given by Doron Zeilberger, because that sounds like him.

[Anonymous No.10055779]

>>10049889
real world applications are for chumps, but that aside, just look for external texts that go in depth with the topics. Search the archives here, archives on reddit, etc. and find one people seem to agree is useful

[Anonymous No.10055956]

>>10054825
Someone just got dumped

[Anonymous No.10055983]

>>10054825
So you fucked her a bunch of times and realized you have to keep talking to her if you want to continue fucking her so you decided to stop fucking her.. is what you're saying. Story as old as time itself.

[Anonymous No.10055992]

>>10055266
Zagier seems to be a bit like this, but he always has a point so I doubt anyone cares.

[Anonymous No.10056003]

>>10054825
>he fell for the vaginal jew
I thought mathematicians were smart

[Anonymous No.10056019]

>roll four six-sided dice (sides are 1 - 6)
>remove the lowest rolled dice and keep the remaining 3
How do I calculate the mean and median? i forgot what mode means so i won't even ask

[Anonymous No.10056079]

>>10056019
Mode is the most frequent outcome. Mean is the average. Median is listing all the numbers in order by size and picking the middle one

[Anonymous No.10056150]

What is the baby Rudin of Differential Equations?

[Anonymous No.10056202]

new grad here

Is it okay to copypasta entire paragraphs from other paper (with references of course) since if I write in my own words I'd write exact same thing with slightly worse grammar?

[Anonymous No.10056206]

>>10056202
No, if you're going to do that just refer to it obliquely ("as Author discusses, studying math is a total fucking meme etc etc etc").

[Anonymous No.10056241]

We can think of [math]e^x[\math] as the unique function that stretches the real line in such a way that multiplication becomes addition. Can this idea be generalized?

[Anonymous No.10056245]

We can think of [math]e^x[/math] as the unique function that stretches the real line in such a way that multiplication becomes addition. Can this idea be generalized?

[Anonymous No.10056250]

>>10056241
Generalised in what way. e^(a+b)=(e^a)(e^b) isn't limited to the reals, it also applies to complex numbers and (in some cases) matrices (specifically, if X.Y=Y.X then e^(X+Y)=(e^X)(e^Y)).

[Anonymous No.10056255]

>>10043248
go away

[Anonymous No.10056258]

>>10054825
It's your own fault. Anthropology students are notoriously dumb. The field was coopted by ideological nutcases decades ago, so only retards study anthropology nowadays. You could have just as well started dating a gender studies major.

[Anonymous No.10056263]

>>10056250
Sorry, remade my post because I messed up the math tag.

I mean generalized to other operations. I'm mostly just musing, I haven't sat down and thought very hard about any of this (yet).

[Anonymous No.10056290]

>>10056263
Look up abstract algebra

[Anonymous No.10056299]

>>10056290
Friend I did my honors thesis in algebra, I'm not sure it's the best way to think about this.

[Anonymous No.10056334]

>>10056245
What do you mean?
Any exponential function makes multiplication addition.

[Anonymous No.10056347]

>>10056334
You're right, my mistake. There's probably something analytically special about image of the reals under exponentiation by e but that's far from my area of study.

Are non-rational exponents even definable without appealing to e anyway?

Also I found this
http://paureahack.blogspot.com/2016/06/supersum-subproduct.html
which discusses how the various operations are related to each other. Interesting stuff.

[Anonymous No.10056354]

>>10056347
>Are non-rational exponents even definable without appealing to e anyway?
I don't see why not. Just use the limit of a sequence of rational exponents approaching whatever exponent you want.

[Anonymous No.10056355]

>>10056347
Also a continual source of amazement for me is how quickly the nice algebraic properties are lost as you "grow" a concept. Exponentiation loses commutativity and tetration loses associativity, and I imagine if you kept going you'd continue to lose more obscure properties. Same thing as you increase the dimension of a division algebra. There seems to be a very small middle ground where concepts are "large" enough to be interesting but small enough to still be structured.

[Anonymous No.10056357]

What's the beginning of maths? What's the end point?

[Anonymous No.10056359]

>>10056357
Homotopy type theory
Homotopy type theory

[Anonymous No.10056364]

>>10056357
the creation of first order logic, be it divine or mundane

when the theories become so complicated its impossible to master them within a lifetime, making further progress impossible

[Anonymous No.10056403]

>>10056357
zero and infinity

[Anonymous No.10056557]

>>10056357

[Anonymous No.10056749]

>>10056364
>when the theories become so complicated its impossible to master them within a lifetime, making further progress impossible
I find it interesting to think about whether we will ever reach this point or not. We're certainly very far away right now. Most mathematicians are competent enough to do work in at least 1 or 2 fields by the time they're 25 or so, and this is under an extremely poorly optimized system where they don't really start doing nontrivial math until 17 or 18 years old. A few years could be shaved off that if non-meme high school math education was more readily available.

But I think it's more likely we'll just do what we've been doing and continously trim off parts of math that have become less relevant. Analysis in the 1800s and early 1900s was a whole zoo of special functions that nobody gives a shit about today. Few people bother much with elementary geometry anymore either.

[Anonymous No.10056778]

When x approaches infinity, what's the limit of (2/7) to the x-th power?

[Anonymous No.10056783]

>>10056150
Evans

[Anonymous No.10056784]

>>10056778
>When x approaches infinity, what's the limit of (2/7) to the x-th power?
What have you tried?

[Anonymous No.10056790]

>>10056784
Isn't it supposed to be trivial? There must be a formula I forgot.

[Anonymous No.10056800]

>>10056557
>one-time pad decryption is the pinnacle of mathematics
it's either trivial or completely impossible, depending on whether you have the key.

[Anonymous No.10056807]

>>10056557
this is so fucking old

[Anonymous No.10056815]

>>10056557
Synplectic geometry is genius level? Physicists must be doing something right.

[Anonymous No.10056851]

>>10056790
How can be something other than 0?
Maybe if you put your fraction in the form 1/(a^x) you can see that you can make it arbitrarily close to 0 by increasing x.

[Anonymous No.10056869]

>>10056851
The full expression I'm trying to calculate is [math]\lim_{n\to\infty}\sum_{k = 1}^{n} \left ( \frac{2}{7} \right ){}^n[/math].

[Anonymous No.10057090]

>>10056869
Isn't your series converging to 4/10?

[Anonymous No.10057126]

>>10056557
>calculus and trig below complex numbers
>vectors way below matricies
Huh? Also
>tfw Engy grad and never used anything below the serious math line

[Anonymous No.10057127]

>>10057090
How do you figure? I'm stuck because I don't know where to start on decomposing that limit.

[Anonymous No.10057221]

>>10042555

>an integer b divides integer c if there exists an integer a such that ab=c

>set a = b = c = 0. Then 0 divides 0, for 0*0=0

>mfw it is possible, in prosaic terms, to speak of a zero-case in which zero divides a number, due to its function as multiplicative annihilator

>division by zero is possible

[Anonymous No.10057227]

>>10057221
>>division by zero is possible
https://en.wikipedia.org/wiki/Wheel_theory

[Anonymous No.10057265]

>>10057227

>wikipedia

[Anonymous No.10057340]

>>10057221
There's a difference between an integer dividing another (a purely multiplicative property) and preforming division with an integer (an appeal to a multiplicative inverse)

[Anonymous No.10057350]

>>10048427
>A simple derivation of the Riemann hypothesis from supersymmetry

[Anonymous No.10057449]

>>10056258
this, played yourself
social sciences are a coin-flip between tolerable and suicidal

[Anonymous No.10057620]

>>10056869
First, I suspect that the exponent should be k, not n.

As for how to calculate the sum:
S=2/7 + (2/7)^2 + (2/7)^3 + ...
(2/7)*S=(2/7)^2 + (2/7)^3 + (2/7)^4 + ...
=S-(2/7)
=> (5/7)*S=(2/7)
=> S=2/5
In general, the sum of an infinite geometric series is a/(1-r) where a is the first term and r is the ratio.

[Anonymous No.10058267]

>>10048427
this is nonsense
>if (.5-iλ) is a zero, (.5+iλ) is a zero, therefore all zeros have real part .5
that simply doesn't prove the hypothesis
in fact the entire jump of logic from 20 to 21 is illogical

[Anonymous No.10058334]

>>10058267
What did you expect from retard pajeets who submit their shit to gen maths? The time you wasted reading their shit is probably worth more than their annual salary.

[Anonymous No.10058383]

Can I get a bit of help. I've been doing well in my Digital fundamentals class, actually had a 100 on all homework until the test, which covered bolean algebra simplification. Does anyone have anything that could help me out here? I haven't done algebra in nearly 15 years and this shit got me a 55/100 on the test.

[Anonymous No.10058494]

What did latex mean by this

[Anonymous No.10058501]

>>10058494
Ignore all instances of homeomorphic in that file as misspelled

[Anonymous No.10058514]

>>10058494
That's not latex that's the windows dictionary missing the word.

[Anonymous No.10058532]

>>10058514
>windows

>>10058494
Found your problem.

[Anonymous No.10058553]

>>10058532
To be fair my linux /dict/words doesn't even have homomorphism

[Anonymous No.10058576]

>>10058525
Is he right?

[Anonymous No.10058602]

>>10058576
maybe but I'd rather kill myself than study finmaths or """business""" so I'm going to enjoy my comfy time with pure maths. If I fail to make it a career I'll just go back to wageslaving as a software dev. Failing that I have autismbucks and my (very well-off) parents.

Overall I think that kind of view is really depressing desu, you should be able to study what you want, that's the whole fucking point of universities, they're supposed to be centres of learning not extended job training. If you need more education than provided by public schooling to succeed in the modern economy then add more public schooling, stop fucking with the university system.

I realize I'm really lucky to be able to take that view, the system is still fucked though.

[Anonymous No.10058604]

>>10042555
How the fuck am I meant to solve this? I understand the fundamentals but my shit book doesn't even go over how to solve this specific type of problem. I can't even find a similar enough problem or example.

[eqn]
f(x)=\frac{cos(x)}{1-e^{ax}}
[/eqn]
*where a is a constant real number

I get it to this:
[eqn]
f'(x)=\frac{(1-e^{ax})(-sin(x)) - cos(x)\frac{d}{dx}(1-e^{ax})}{(1-e^{ax})^{2}}
[/eqn]

In particular I'm confused by what to do with the [math](1-e^{ax})[/math]. For the first one, I guess that you distribute the [math]-sin(x)[/math] but for the second, why is the derivative [math]-ae^{ax}[/math]? Why does (a) get multiplied by the base but stay in the exponent? (I looked up the answer on Wolfram). Then for the denominator, the signs get flipped to [math](e^{ax} -1)^{2}[/math]

[Anonymous No.10058614]

Let [math]f:\mathbb{A}\to \mathbb{B}[/math] be a function between sets, and:
[math]a\in \mathbb{A}[/math]
[math]A \subset \mathbb{A}[/math]
[math]\mathcal{A} \subset \mathcal{P}(\mathbb{A})[/math]

I want to 'lift' [math]f[/math] to higher collections, like you would with 'map' in programing. ive seen 3 notations for doing it once:
[math]f(A) = f_*(A) = f[A] = \{f(a)|a \in A\}[/math]

I also need more levels, like:
[math]f( \mathcal{A}) = f_{**}( \mathcal{A}) = f[[ \mathcal{A}]] = \{f(A)|A \in \mathcal{A}\} = \{\{f(a)|a \in A\}|A \in \mathcal{A}\}[/math]

Is there a name for what im calling 'lifting', or 'mapping'? And which notation is best if I need to make the level obvious, [math]f_*(-)[/math] or [math]f[-][/math]?

[Anonymous No.10058615]

>>10058604
>why is the derivative −ae^ax
Have you been taught that e^f(x) = f'(x)e^f(x), where f(x) is a function (in your case ax). Which really follows from the chain rule and the fact that d/dx e^x = e^x.

[Anonymous No.10058618]

>>10058604
let f(x)=e^x. It is known that f'(x)=e^x. If h(x)=ax, then h'(x)=a.

Now if g(x)=e^ax, you can write g(x) = f o h(x), so by the chain rule, g'(x)= f'(h(x))h'(x)= (e^ax)a

[Anonymous No.10058619]

>>10058614
f(A) is common enough notation for a set, if you're doing nested sets you should probably define what you mean as you've done in your second example.

[Anonymous No.10058623]

>>10058615
I'm self teaching but yeah one of the chapters this worksheet is based on introduces the chain rule, guess I need to read ahead before I proceed.

>>10058618
That's an excellent explanation thank you. I actually got the answer right for what the book was expecting. Wolfram it seems went above and beyond (probably cause I didn't declare a as a const. real number).

[Anonymous No.10058626]

how easy was it for u guys to understand curl....

was it GGEZ or did u have a hard time...

[Anonymous No.10058640]

>>10058626
As a vague concept of infinitesimal rotation I thought it was pretty simple. I haven't looked at it from a more rigorous view though

Fuck I really need to learn some differential geometry.

[Anonymous No.10058644]

>>10058626
circulation at a point, similar to how derivative is slope at a point.

[Anonymous No.10058844]

How do you find the fraction of a value? For instance if you have 12.533333...., what's the smallest fraction for it?

[Anonymous No.10058850]

>>10058844
I know it's 188/15 but how would I find out without guessing/knowing beforehand?

[Anonymous No.10058861]

>>10058844
12.5333 =
125.333/10 =
(125+0.333)/10 =
125/10 + 0.333/10 =
125/10 + (1/3)/10 =
125/10 + 1/30 =
375/30 + 1/30 =
376/30 =
188/15

[Anonymous No.10058891]

Any of you senpais got any insight about the Hardy-Littlewood Maximal Function?

Seems like it takes a function and a point, finds the sphere centered at x such that f is absolutely maximized, (relative to the volume of the sphere?), and spits out the integral of f on this sphere

[Anonymous No.10058927]

What book should I take to start with algebraic geometry, if I finished Homology/Homotopy theorie courses, and studied a bit of rational homotopy theorie?

[Anonymous No.10058935]

>>10058626
It's easy af, if you look at it as an integral.

[Anonymous No.10059476]

>>10058927
AG is much different than AT, so you might do well in starting with an "easy" into book to get intuition before schemes. Perhaps something like Fulton's Algebraic curves or Shafarevich Basic AG 1+2. Then you can use Vakil's notes

[Anonymous No.10059480]

>>10058927
Conmutative Algebra book

[Anonymous No.10059491]

>>10058927
It depends how deep into algebraic geometry your goals are. I think the best-general purpose suggestion is Shafarevich. It's a good middle ground between an accessible intro and actual legitimate algebraic geometry, and the writing is excellent. Even for people who want to segue into meatier things this is a great starting point.
If you only want to take a quick look at algebraic geometry's ass there's a cute little 150-ish page book by Karen Smith (et al) which is a much faster way to just get an idea what a variety is and why anybody cares, but it's not really going to take you anywhere very serious.

[Anonymous No.10059517]

If [math]\lim |x_{n} - y_{n}| =0 [/math] for real valued sequences, [math]x_{n},y_{n}[/math], is it true that [math]\lim |x_{n} - y_{n_{k}} | =0 [/math] for some subsequence of [math]y_{n}[/math] ?

[Anonymous No.10059532]

>>10059517
Yes if you allow yourself the stupid solution of taking the entire sequence as your "subsequence". If you do not do this, then the answer is sometimes no.

[Anonymous No.10059538]

>>10059517
...yes? Or are you not counting a sequence as being a subsequence of itself?
Otherwise no, take x_n = y_n = n

[Anonymous No.10059544]

>>10059532
>>10059538
proper subsequence, as in not including the original sequence as a subseqeunce.

[Anonymous No.10059578]

How much will grad schools care about bad grades in humanities classes

[Anonymous No.10059586]

>>10059578
I'm talking out of my ass but to me personally it suggests you're one of those people who is utterly unable to communicate ideas effectively. Why did you do poorly in your humanities classes anon?

[Anonymous No.10059590]

>>10059586
not him but because i'm a major autist who can't even talk to a cashier without sweating

[Anonymous No.10059594]

>>10059590
I can relate anon, I've had pretty bad social anxiety in the past. But you need to get over it if you want to do research, you'll be talking to people all the fucking time, and if you want to get anywhere you need to make friends with some of them.

[Anonymous No.10059595]

>>10059594
>But you need to get over it
that doesn't really help my situation here

[Anonymous No.10059598]

>>10059595
I'm not a therapist anon, not much I can do. Or if you're talking about your grades you should find some way to spin it or take more classes to pad it out if possible.

[Anonymous No.10059606]

>>10059586
i just turned in my first paper for this intro philosophy class and im paranoid the TA will see it as the cobbled-together shit that it is

[Anonymous No.10059662]

>>10058626
The concept of curl is pretty easy, I'll use an analogy to illustrate it. Imagine you placed a ball into river and kept the position fixed, only allowing it rotate. The ball will then rotate, but how much? Well when we remember that the flow of the water can be described by a vector field we imagine that this field will tell us. If you look at the vectors at the boundary of the ball, as those are the ones that influence the direction of rotation, the it's easy to see that any component of the vector that acts normal to the surface of the ball doesn't affect the rotation. So now we just have to collect the components of the vectors in the vector field that are tangent to the surface and add them up. However to add these quantities you first realize that the vector field is defined on the whole space, so an integral is required. So you need to integrate the vector field. It's also easy to see that once you sum all the vectors together the rotation must occur about some axis. But this is still defined over some region and the curl is defined at a point, so what you do is shrink the ball and define the curl as the limit as the radius of that ball goes to zero. The integral tells you the magnitude of the rotation and the vector tells you the axis of rotation.
[math]{\displaystyle (\nabla \times \mathbf {F} )\cdot \mathbf {\hat {n}} \ {\overset {\underset {\mathrm {def} }{}}{=}}\lim _{A\to 0}\left({\frac {1}{|A|}}\oint _{C}\mathbf {F} \cdot d\mathbf {r} \right)}[/math]

[Anonymous No.10059703]

i have learned multivariate calculus TWICE (once in high school once in uni) and i've forgotten most of the concepts AGAIN
how do i keep this shit in my head

[Anonymous No.10059718]

>>10058891
>Seems like it takes a function and a point, finds the sphere centered at x such that f is absolutely maximized, (relative to the volume of the sphere?), and spits out the integral of f on this sphere
Basically, it might help to think about it in terms of densities. If f(x) describes the density of a material at some point x then taking the integral over some ball gives you the mass, dividing by the volume of the ball gives you the average density of that ball. So the maximal function then takes a density function and tells you the maximum average density at every point.

[Anonymous No.10059923]

Lang's Algebra book y/n

[Anonymous No.10059929]

>>10059517
x_n = y_n = (-1)^n
n_k = 2k

[Anonymous No.10059995]

>>10059923
>Lang's Algebra book y/n
n, Lang is a meme.

[Anonymous No.10060029]

>>10059995
How so?

[Anonymous No.10060059]

>>10059703
Well if you just read without doing many exercises, of course you'll forget.

[Anonymous No.10060062]

>>10060059
i did plenty of exercises please believe me
i just haven't done anything with it in a year

[Anonymous No.10060078]

>>10060029
>How so?
Why don't you read any of his works and find out?

[Anonymous No.10060096]

Anyone else read 2hu wrestling doujins here?

[Anonymous No.10060121]

>talked to my adviser because i didnt wanna do what he liked on knot polynomials
>assigned me to work on quartic plane curves and rational points
yes lads, back on track

[Anonymous No.10060145]

>>10060121
Glad to here things are working out anon. If you're working close to enumerative geometry you may want to try your hand at some cool mathematical physics. Seems there's a lot of overlap between objects in number theory/algebraic geometry and mathematical physics these days. Just a suggestion since I personally find these things cool.

[Anonymous No.10060180]

Given, [math]\epsilon>0[/math], [math]A\subseteq\mathbb{R}[/math] and a closed set [math]F[/math] such that [math]F\subseteq A[/math] and [math]m^{*}(A\setminus F) < \epsilon[/math], how do I show [math]A[/math] is Lebesgue measurable.

[Anonymous No.10060216]

If [math]\{A_{n} \}[/math] is a collection of Lebesgue measurable sets with [math]\sum m(A_{n})<\infty [/math] how do I show [math]m\left(\bigcap_{n=1}^{\infty} \bigcup_{k=n}^{\infty} A_{k} \right) =0[/math]

[Anonymous No.10060292]

jusdt got my first linear algebra 1 exam back ffs professor is a 30 year old /sci/ poster

[Anonymous No.10060304]

>>10060292
Why is your writing so bad? How old are you?

[Anonymous No.10060344]

What do I need to into Calculus of Variations?
I came across it in Differential Geometry and I want to know more. Seems like an interesting next level of abstraction.

[Anonymous No.10060353]

>>10060216
Well, we know for [math]\sum m(A_{n})<\infty[/math] to converge the terms [math]m(A_{n})[/math] must either be non-zero for only a finite number of [math]A_{n}[/math] or the measures of the sets [math]A_{n}[/math] must go to zero sufficiently quickly. From there it should be clear, at least at the intuitive level, why
[math]m\left(\bigcap_{n=1}^{\infty} \bigcup_{k=n}^{\infty} A_{k} \right) =0[/math] since this amounts to [math]m\left(\bigcap_{n=1}^{\infty} \bigcup_{k=n}^{\infty} A_{k} \right) =\lim m\left(\bigcap_{n=1}^{j} \bigcup_{k=n}^{\infty} A_{k} \right)=\lim m\left(\bigcup_{k=j}^{\infty} A_{k} \right)[/math]
This isn't rigorous, but it's not too hard to make it.

[Anonymous No.10060398]

>>10060344
In terms of math, fairly little. Basically just elementary analysis. Might be helpful if you know rudimentary facts about functional analysis too but I wouldn't worry about it if you don't.
Some background in mechanics would be very helpful for intuitive purposes.

[Anonymous No.10060416]

>>10060398
Thanks. What's a good intro text? I understand the brachistome problem and basic analysis, but haven't done functional analysis at all.

[Anonymous No.10060459]

>>10060292
why do you think he's a /sci/ poster?

[Anonymous No.10060668]

>>10060078
You're the one who literally told me to not bother my dude

[Anonymous No.10060746]

>Proof. Trivial

>Spent 20 mins looking at paper and still don't understand

[Anonymous No.10060754]

>>10059929
Not a disproof, OP's prop was that there exists an subsequence which approaches x_n not that all subsequences do

[Anonymous No.10060757]

>>10060746
Post it here so we can judge you

[Anonymous No.10060766]

Why do people like algebraic geometry again? I am, admittedly, an undergraduate brainlet, but it seems like a field dedicated to fucking around with boring equations and trying to find integral solutions or whatever the fuck they do. Explain the appeal /mg/.

[Anonymous No.10060769]

>>10042896
LMOFA!
The Yukarifag is a fucking moron, ask him anything outside of TQFT (Nothing important - failed theory) and he will shit his pants.
He once tried to argue that all Jacobians are square matrices.

[Anonymous No.10060780]

>>10060769
>him

[Anonymous No.10060807]

>>10060780
Shut up faggot

[Anonymous No.10060819]

>Learning topology
>rewrite definition of a topology to be more general
>notice I dont need the set its on
>get rid of it
>notice the subsets is just a partially ordered set with some conditions on the operators
>check and see they form a lattice with some constraints
>excited because it looks better than the normal definition
>google to see if anyone else did it before
>pointless topology is already a thing

Why dont they teach pointless topology in introduction classes? is it actually pointless (pun intended)?

[Anonymous No.10060823]

>>10060766
that's exactly what it is but, because it has now shrouded itself in arcane language, everyone has convinced themselves that it is the deepest field of study in the mathematical world

[Anonymous No.10060825]

>>10060754
I don't understand the problem here. |x_n - y_n| approaches zero but |x_k - x_{n_k}| doesn't

[Anonymous No.10060836]

>>10060819
Most people get their first taste of topology from studying the real line and building up to basic real analysis. The usual point set topology just matches what people usually think of and helps them match what they may view as abstract results to more tangible objects. Not saying this is the correct way of learning the subject but imagine this is the mentality.

[Anonymous No.10060917]

>>10060819
>Why dont they teach pointless topology in introduction classes? is it actually pointless (pun intended)?
It's mostly of interest to computer science people and constructive mathematicians. It's not pointless per se but it's not the usual way of doing topology.

[Anonymous No.10060986]

>>10060769
>He once tried to argue that all Jacobians are square matrices.
Hey, Scholze once tried to use Faltings' theorem to prove a result that only required elementary knowledge of the theory of rational heights.

[Anonymous No.10060988]

>>10060807
>faggot
Why the homophobia?

[Anonymous No.10060992]

>>10060988
Because homosexual intercourse causes aids and hiv.

[Anonymous No.10061005]

>proof by induction

[Anonymous No.10061018]

>>10060992
That statement is false and it is insufficient to establish homophobia. Please review your basic proof techniques, anon. /mg/ is a rigorous thread.

[Anonymous No.10061025]

>>10061005
>proof by contradiction

[Anonymous No.10061029]

>>10061018
Is 68% of all diagnoses HIV in America are from gay and bisexual men not rigorous enough for you? This is despite the fact that gay and bisexual men only make up 4% of the US population.

[Anonymous No.10061037]

>>10061029
>not rigorous enough for you
No. To be clear. I don't actually care about your position. Just your lack of rigor.

Here is your argument with the details abstracted out:
>I subscribe to ideology Y
>>Why tho?
>Because A causes B
>>That statement is false and insufficient to establish your subscription to Y.
>A is correlated with B therefore A causes B.

[Anonymous No.10061107]

>>10061037
Fucking sperg.

[Anonymous No.10061317]

>>10060825
Because you just gave an example of a non-convergent subsequence, you didn't prove that one doesn't exist.

[Anonymous No.10061357]

>>10061025
Sometimes you need them tho
Though 90% of the undergrad contradiction proofs I see are actually just proof by contraposition

[Anonymous No.10061577]

>tfw too busy to study math
I want this meme internship to end

[Anonymous No.10061692]

>https://en.wikipedia.org/wiki/Cantor_function
Analysis was a mistake
The reals are trash

[Anonymous No.10061854]

>>10061692
You think that's bad, check this out
https://en.wikipedia.org/wiki/Conway_base_13_function

[Anonymous No.10061857]

Why is integral calc so hard, guys? It seems no matter how many rules I learn, there's always some obscure one that I forget, and it ruins the rest of the problem. I suppose tons of practice is really the only answer to this.

[Anonymous No.10062013]

>>10061857
Alternatively, you could develop problem-solving skills.
>>10061025
Those are the best proofs.
>>10059517
Yuh.

[Anonymous No.10062052]

>>10062048
new thread
>>10062048

>>10062048

>>10062048

>>10062048

>>10062048

[Anonymous No.10062185]

>>10062013
>Alternatively, you could develop problem-solving skills.
wut

most useful integrals are not doable by humans

that's just how integrals are

[Anonymous No.10062278]

>>10061857
Most Calc books have a section in the integration techniques chapter of 50+ integrals that can be solved using one, or a combination, of the techniques taught in the chapter.

If you’re struggling, working every one of these problems until you get them right without fail is the main way to get past Calc II’s integration portion.

[Anonymous No.10062581]

>>10042555
as i progress with the degree i find it harder and harder to find PDFs of the books for my courses. Is there any trick to it? Is there some kind of maths PDFs source out there?