/mg/ - maths general

[Anonymous No.10698366]

Please be my advisor edition.
Talk maths.

[Anonymous No.10698740]

>>10698366
Day 1728
Still waiting for a solution to soliton resolution conjecture. I'm optimistic that I'll die before a proof is found.

[Anonymous No.10698857]

first for motives

[Anonymous No.10698873]

>>10698306
You can use the same parametrization, but the irrational radius is going to show up. If you want to find integer points on an arbitrary circle, you're going to have trouble.

https://en.wikipedia.org/wiki/Gauss_circle_problem

[Anonymous No.10698937]

Threadly reminder to work with physicists.

[Anonymous No.10698950]

what meds are you guys on?

for me it's 20mg escitalopram and 0,25mg xanax

[Anonymous No.10698967]

What is your latex configuration?

[Anonymous No.10698972]

>>10698937
>>10698950
>>>/trash/

[Anonymous No.10699006]

>>10698937
stop posting this every thread
physicists are a plague
>>10698950
not a disgusting addicted druggie, thanks

[Anonymous No.10699013]

>>10699006
>not a disgusting addicted druggie, thanks

I've social anxiety

[Anonymous No.10699033]

>>10699013
Is xanax good for that? I take ssri for anxiety and depression

What's weird is my anxiety is competely generalized, I could be anxious about literally anything: social situation, job security, etc but I get the worst panic attacks when I think about the nature of reality, consciousness, space, time, and what we really are on this plane of existence

[Anonymous No.10699039]

>>10699033

Xanax will stop you from commiting suicide but it renders you pretty much useless -- drops your IQ severely.I take it only when it's really necessary.

[Anonymous No.10699218]

>>10698366
tfw can't even pass basic high school maths
Honestly I don't even know why I browse this board

[Anonymous No.10699380]

Everyone said calc 3 is easier than calc 2.....its not and im currently in hell in calc 3. sure its a summer class but im ready to kms. How do i get past this

[Anonymous No.10699388]

>tfw literally doing a fucking prealgebra textbook for children so I can better understand Morris Kline's History of Mathematics and learn math historically from the Greeks onward
>tfw I'm hoisting myself by the ballbag and hurtling straight into calculus whether I like it or not
>tfw from there I'm going on to college math and theoretical math at as reasonable a pace I can manage
>tfw I will get all my math knowledge back and have fun being a math knowing guy or I will die trying

NO MORE FUCKING AROUND

[Anonymous No.10699421]

>>10699013
>>10699033
>>10699039
All dumber and have less potential than
>>10699218
>>10699380
>>10699388

Sorry druggies, your time is up. It's pathetic that you rely on a chemical to "succeed" in math and life.

[Anonymous No.10699427]

>>10699421
>Sorry druggies, your time is up. It's pathetic that you rely on a chemical to "succeed" in math and life.
*sips coffee*

[Anonymous No.10699429]

>>10699421
what chemical

[Anonymous No.10699439]

>>10699033
take propranolol. Its a beta blocker that tones down the fight or flight response. Has worked well for me.

[Anonymous No.10699440]

>>10699388
>from the Greeks
geometry is a mistake
you may as well try to learn the history of math by following all the classical developments of science and physics

learning math "historically" is just you procrastinating from actually learning math

[Anonymous No.10699442]

>>10699421
>>10699429
oh fuck it's 3:42am and I didn't see the other replies on top my bad

[Anonymous No.10699535]

>>10699380
In for answers, my prof was horrible with explaining any of calc 3 to my freshman self after having an awesome one for calf 2

[Anonymous No.10699583]

>>10699442
Should have used on a certain well-known chemical to give you a heightened sense of reality.

[Anonymous No.10699616]

>>10699380
Calc 3 is supposed to be easier once you get over the 3rd z axis addition to doing derivatives/integrals. What makes it difficult from what I recall is more applied math and into of vectors and that kind of thing. If you suck with applied math, that's why you suck.

Same here, Calc 1 and 2 were easy for me 3 was impossible so I quit. The moment I have to start using math in a world problem, it's over for me I just don't know how to interpret the english into symbols and logic. My logic's sht too.

[Anonymous No.10699724]

>>10699427
I don't drink coffee often, and when I do it's only because I like the taste. I don't care at all for the effect.

[Anonymous No.10699988]

Consider two polynomials, [math]p_a(x) = \sum_i a_i x^i[/math] and [math]p_b(x) = \sum_i b_i x^i[/math] with real coefficients [math]a_i, b_i[/math].

If we know that [math]|a_i| \geq |b_i|[/math] for all i, then what can we say about the roots of [math]p_a[/math] vs. the roots of [math]p_b[/math]?

[Anonymous No.10700003]

Just got this book, time to study analysis over the summer

[Anonymous No.10700044]

>>10699988
Nothing. Multiplying the polynomial (and thus all the coefficients) for a constant c, leaves the roots unchanged. So, for example, if p_a has positive coefficients [math]p_b=c\cdot p_a[/math] for some [math]c<1[/math], then [math]b_i<a_i[/math] but the roots are the same. And whatever roots the two polynomials have, if coefficients are positive you can replace [math]p_b[/math] with [math]c\cdot p_b[/math] for some sufficiently large c, until you get [math]b_i<a_i[/math] for all i.

[Anonymous No.10700047]

>>10700044
*Sufficiently small

[Anonymous No.10700052]

>>10699616
>A whole course on 2 var calculus
>Another on 3 var calculus

[Anonymous No.10700079]

I'm going to do a minor in maths and I have to pick one of these courses for the first period of next year:
>Analysis on manifolds
>Basic number theory
>Functions and series
>Group theory
>Measure and integration

Which one of these is doable for a brainlet? Which ones are not interesting?

[Anonymous No.10700094]

>>10700079
>Analysis on manifolds
Do not attempt
>Basic number theory
>Functions and series
>Group theory
>Measure and integration
Depends on your education and interests; it's a broad list. Do some googling
For me, group thy is the more interesting topic here

[Anonymous No.10700102]

>>10700094
Thanks
I'm doing a double brainlet bachelor in cs/informatics.
Cryptography is interesting, but I mainly picked this minor out of the interest in mathematics I had since highschool.

[Anonymous No.10700103]

>>10700079
>analysis on manifolds
You probably don't have the topological background. Not even considering multilinear algebra.
>number theory
Comfy.
>functions and series
Fuck if I know what that is.
>group theory
LMAO YOUR UNI LETS A NIGGA FINISH A MATH MINOR WITHOUT KNOWING THAT.
>measure and integration
You still don't have the topological background.

[Anonymous No.10700120]

>>10700103
>LMAO YOUR UNI LETS A NIGGA FINISH A MATH MINOR WITHOUT KNOWING THAT.
Yeah I guess its just really dumbed down maths. We only have 2 mathemtic minors; "mathematics for physicists" and "mathematics for non-physicists" and since I'm not a physics major I can only do the other one.

[Anonymous No.10700122]

I need help
I have decided about two months ago i would learn math from the beginning, since then i studied a lot, and i seem to understand and make most of the exercises.
The problem is : i forget all of it and need to study it again, just now i was trying to do some exercises from 2 weeks ago and seemed like i dont know how to do it
Is it normal ? What should i change for me to really learn stuff

[Anonymous No.10700126]

I'd like to study numerical analysis this summer, what are the prereqs for a smooth learning experience?

[Anonymous No.10700137]

>be EE student
>took introductory complex analysis at the math faculty
>failed three problems on the exam due to not being able to simplify algebraic expressions
:(
Do math students just know the trigonometric identity for everything?

[Anonymous No.10700143]

Is Wilbur Knorr's reconstruction of initial version of incommeasurability proof generally considered legit around the block? Asking for a friend.

[Anonymous No.10700158]

>>10700137
If you mean double angle, half angle etc just derive them from Euler's formula

[Anonymous No.10700172]

>>10698967
Man, Luke's rice made my transition from windows to arch much easier. Thank God this man exists.

[Anonymous No.10700184]

>>10700079
Number theory and group theory. Thank me later.

[Anonymous No.10700220]

>>10700184
Literally anything but this

The measure and integration ones are extremely important but also some of the hardest undergrad courses

Take anything relating to analysis

[Anonymous No.10700242]

>>10700220
He asked for "doable for a brainlet". He'll fail spectacularly if he goes the anal route.

[Anonymous No.10700429]

>>10698967
Luke's great! Although I do not think his snippet setup is the best alternative for mathematical writing (I've replicated it for math). I think something like this is better:
https://castel.dev/post/lecture-notes-1/
https://castel.dev/post/lecture-notes-2/
>What is your latex configuration?
What you want to know? .vimrc stuff or LaTeX preamble/macros?

[Anonymous No.10700444]

autocmd BufEnter *.tex nnoremap <Space>c :lcd<Space>%:p:h<CR>:w<CR>:!pdflatex<Space>%<CR><CR>
autocmd BufEnter *.tex nnoremap <Space>p :lcd<Space>%:p:h<CR>:!zathura<Space>%:r.pdf&<CR><CR>

[Anonymous No.10700449]

neovim > vim.

[Anonymous No.10700473]

>>10700429
I'm considering something more comfortable than texstudio, possibly via terminal, and I'm trying to understand if vim could be good

[Anonymous No.10700476]

>>10700079
the best courses there are analysis on manifolds and measure and integration, but they are also the toughest.
basic number theory is probably fun and not too hard, but i hate it
group theory is something you should have some experience with but i also hate it
do you have more info on what functions and series is? fourier analysis or something?

[Anonymous No.10700516]

>>10700476
Thanks for your input.
>do you have more info on what functions and series is? fourier analysis or something?
Its kind of a weird course since its also the only one that isnt given in English. The course page does mention Fourier analysis, and power series. Also something about "Gibbs phenomenon" and limits.

[Anonymous No.10700517]

>>10700449
Man of taste.

[Anonymous No.10700543]

Wtf algebra isnt fun anymore.
Im in my 4th semester of algebra now (2 semesters of linear algebra, 1 semester basix field group ring, theory this semester is Nullstellensatz, more ring theory) and I feel like I dont have any intuition any more.
I understand all the proofs' steps but I struggle so hard with the exercises now.
Before when I looked at a problem I would usually get an idea how to solve it by intuition. Now I just cant feel a good strategy to go through the tree of possible things to try anymore and end up blindly trying random things but not solving the exercise.
It feels like Im already supposed to know how northerian rings and varieties etc. behave. How the fuck can I expect that an atrinian ring can be written as a product.
Even if I only have to only apply a few theorems consecutively I dont see it.

[Anonymous No.10700544]

>>10698967
AUCTeX and org-mode. I am a self-respecting white man after all, not a vim-using amerimutt.

[Anonymous No.10700548]

>>10700473
I would strongly recommend learning vim if you are planning on writing a lot for years to come, may it LaTeX, code or just plain text in general. It takes a while to really get the hang of it, thus it's not worth it in the short run. There seems to be a few (neo)vim+LaTeX masterace in thread, so just ask any question and we'll get you going.

[Anonymous No.10700553]

>>10700516
Oh, that class seems fun too then. I quite like that class.
If you enjoyed your analysis/calculus a lot, you'd want one of the manifolds, series, or measure classes. Probably series.
If you enjoyed linear algebra more, or you tend to like competition style problems, you'll probably enjoy group theory or number theory.

[Anonymous No.10700555]

>>10700543
you weren't doing real algebra before. now you are. you don't like it, it's okay. go with something else.
i felt exactly the same way and i am a devoted analyst now.

[Anonymous No.10700558]

>>10700555
Im thinking Ill do that too now but im still wondering why I feel this way because I wouldnt expect some brains to just be better at analysis and some better at algebra. Do I just need to study the results more? Or the proofs? Or maybe my algebra class is just hard while my analysis class is babby tier I have no idea

[Anonymous No.10700562]

>>10700548
I think I can learn vim or whatever on my own. Say I'm using vim. How do you pair it with tex in such a way that you can compile often without need to switch between five terminals?

>>10700544
Explain yourself

[Anonymous No.10700587]

>>10700562
>How do you pair it with tex in such a way that you can compile often without need to switch between five terminals?

First you need install a LaTex compiler. If you are on Linux you can install it with simply

sudo apt-get install texlive-full

If you're using biblatex (recommended), you need to download some extra packages for that, but you can easily find these online.

Then you put these >>10700444 two lines in your .vimrc which assigns compiling the document to Space+c and bringing up the pdf in zathura pdf-reader to Space+p. Change out "zathura" for whatever pdf-reader you are using. You can change the bindings to whatever you want that's not already a binding in vim. It's possible to unbind most standard bindings as well.

NB: You might want to remove the last <CR> on each line to be able to always view the non-critical errors from the compilation. And use neovim instead of vim.

[Anonymous No.10700593]

>>10700120
>>10700103
>>10700079
UU? If so don't even bother with anything but number theory or group theory because you will get your shit pushed in by the others.

[Anonymous No.10700594]

>>10700102
If you like crypto, number theory would be relevant to you

[Anonymous No.10700595]

Grothendieck

[Anonymous No.10700602]

>>10700476
>>10700516
First week covers Frechet derivatives, defos not a good starting point for a comp sci student. It's a course that seems to bridge some other courses so it does a lot of things, including some Fourier analysis.

[Anonymous No.10700610]

>>10700587
Cont.

Detailed explanation of Space+c command.
1) Saves the .tex you are currently viewing in vim
2) Change the local current directory to directory of current .tex file
3) Run pdflatex on current .tex file in a terminal emulator inside of vim.

[Anonymous No.10700624]

>>10700593
>>10700602
Yeah, UU. I asked some mathematics majors and they also recommended those 2. Which one would you recommend? Right now I'm leaning towards number theory because of >>10700594.

Do I have to do some pre-work during thr summrr to not get completely exposed?

[Anonymous No.10700632]

>>10700610
>>10700587
Thanks. This is nice.

What about templates?

[Anonymous No.10700633]

>>10700562
>Explain yourself
AUCTeX is superior to anything vim can offer in terms of LaTeX support, just look into it. org-mode is objectively the best and easiest to learn tool for writing notes or documents you convert to LaTeX PDFs, or even nicely formatted HTML to send via mail. helm-bibtex or RefTeX are better than any vim alternative for quickly inserting and managing citations (either using a bibliography file, or directly from arxiv).

Vim is basically a crippled code-editor for pr*grammers. Look into emacs (spacemacs is a good choice for beginners) and AUCTeX if you're a white man and plan on doing any even remotely serious writing.

[Anonymous No.10700646]

>>10700633
I think I'll try both because i find this whole text editing wars childish and embarassing, and because i like to fantisize about f*cking nerdish n*gger pr*grammer girls

[Anonymous No.10700651]

>>10700632
>What about templates?
You wonder how to insert a template to an empty file, or do you want actual templates?

[Anonymous No.10700653]

>>10700646
>text editing wars
Emacs isn't really a text editor. Only illiterate/ignorant pr*grammers think that. It's a general tool for working with text, not something which merely edits it. It's easy to learn too, even my tech-illiterate professor uses it.

[Anonymous No.10700655]

>>10700624
Number theory (actually, elementary number theory instead of basic number theory, meaning it uses elementary methods rather than algebraic or analytic ones) is more accessible but personally I find it dry. It's good if you liked the discrete maths course your dept offers and/or if you plan to do anything involving discrete numerical computations later because you'll learn about a lot of tools.

Group theory is less numeric. It's just as applicable to modern cryptography as number theory is, but if you plan on looking at cryptography you will need both. It's also probably tougher for a comp sci major than the number theory course because you will be required to write a lot of proofs that do not just involve prime numbers but larger "structures". Note that this doesn't mean you're safe from proofs if you choose number theory, most every course from the maths dept revolves around proofs.

You don't really need to review anything, but if you have the time, learn more linear algebra. Matrix groups were used as examples in the group theory course when I took it.

[Anonymous No.10700661]

>>10700633
I actually took a look at AUCTeX right now, and it seems pretty darn nice. Couple it with evil mode and I can have my vim-bindings there too. I will probably switch at some point.

[Anonymous No.10700669]

>>10700651
I don't want to write \documentclass etc etc every time i start a document

[Anonymous No.10700670]

>>10700661
Look into yasnippet for writing snippets too. You can just press a keybinding directly from a .tex file to write new ones. There should also be premade snippets somewhere, but I haven't used them.

[Anonymous No.10700710]

>>10700655
I really appreciate you for writing this anon, thanks.

I'm currently watching this Youtube playlist https://www.youtube.com/playlist?list=PLAvgI3H-gclb_Xy7eTIXkkKt3KlV6gk9_ , so far group theory seems like an interesting course. The 4 axioms don't seem too difficult to understand and implement so far, but I assume thats just the easiest part of the course?

[Anonymous No.10700723]

>>10700669
There are many ways to do this. A simple solution is to bind a hotkey to paste in the contents of a template file when a binding is pressed. For example by

nnoremap \tex :-1read $HOME/.vim/template.tex<CR>

which pastes in the contents of the file at $HOME/.vim/template.tex when \tex is pressed. To minutely improve on this instead do

inoremap <C-l> <Esc>/<++><Enter>"_c4l
nnoremap \tex :-1read $HOME/.vim/template.tex<CR>/<++><Enter>"_c4l

and put <++> at the positions in the template file where you want the cursor to focus. Then you can jump to the next cursor position with Ctrl+l. To have this binding to only work in .tex files, swap out the last line with

autocmd FileType tex nnoremap \tex :-1read $HOME/.vim/template.tex<CR>/<++><Enter>"_c4l

[Anonymous No.10700733]

>>10700670
Very nice, thanks!

[Anonymous No.10700735]

>>10700710
>The 4 axioms don't seem too difficult to understand and implement so far, but I assume thats just the easiest part of the course?
Sure, those conditions define a group, and the group is the basic building block for everything in the course. Everything in that youtube playlist should be covered by the course so click some random videos and see if you like the material!

[Anonymous No.10700774]

>>10700723
Cont.

If you want this to happen automatically on the creation of a new .tex file, you can use

autocmd BufNewFile *.tex -1read $HOME/.vim/template.tex

[Anonymous No.10700784]

>>10700735
Thanks, I'll do that. I'll probably also just schedule a meeting with the study advisor.

[Anonymous No.10700787]

>>10700558
>wouldnt expect some brains are better at analysis and some are better at algebra
that's just the way it is, they're significantly different in the styles of problem solving and intuition that they require.
this should be evident from the simple fact that one is filled with equalities while the other is filled with inequalities. algebra is all about studying structure and rigidity while analysis is all about studying bounds and fuzziness.
it's possible your analysis class isn't hard, and you should keep in mind that the commutative algebra and ring shit you're doing is considered by many to be the most dry and boring kind of algebra. but at the same time the flavors of the arguments you see will permeate the entire domain of algebra.

[Anonymous No.10700793]

>>10700624
>>10700710
>>10700784
know that number theory and group theory complement one another really well and i think you should take number theory as it might be more relevant and fun than group theory, and then doing your best to learn some group theory on the side. many elementary number theory concepts put group theory into a wonderful and helpful context.

[Anonymous No.10700809]

>tfw have to pick between doing interesting PhD and being poor or become a codemonkey but being rich

[Anonymous No.10700896]

>>10700809
Define rich.

[Anonymous No.10700921]

>>10700896
having enough assets to live comfortably without working

[Anonymous No.10700974]

what fields in applied mathematics/mathematical physics are good to go into for PhD?

something with low hanging fruit
not fluid mechanics

[Anonymous No.10701212]

>>10700633
Hey this is pretty fun, although there's a thousand keyboard shortcuts to remember. I've been fiddling with [math]\mbox{general tools for working with text}[/math] instead of preparing research proposals. You should be happy.

[Anonymous No.10701226]

>>10701212
but why does this happen when I C-c C-p C-d after having C-c C-a?

[Anonymous No.10701277]

>>10700220
>The measure and integration ones are extremely important
>measure and integration is more important than group theory
what in gods name is wrong with analysts

[Anonymous No.10701293]

>>10701277
Measure and integration is the basic grounding of real analysis, alongside topology.

[Anonymous No.10701357]

>>10701212
>although there's a thousand keyboard shortcuts to remember
Install which-key, it helps a lot with highlighting possible completions for some shortcut.

>I've been fiddling with general tools for working with text instead of preparing research proposals.
Yeah, it's a good couple of days or so of gradual customization until you've got the basic workflow exactly as you want it.
>but why does this happen when I C-c C-p C-d after having C-c C-a?
No idea. I usually don't preview the entire document, instead I do C-c C-p C-s to preview just the section, and C-c C-c to compile. Maybe try that? C-c C-a seems to take a lot longer for me, no idea what it does differently.

[Anonymous No.10701428]

>>10701277
group theory is a fucking meme for utter moronic shitheads
DUHHHHHH FINITE GROUPS HUURURURRRRR DUDUURRRRRR CENTRALIZERS BLUUUUGHHHHHHHHH DERIVED SERIES OF A SOLVABLE GROUP
shut the fuck up you math incel

[Anonymous No.10701430]

>>10701428
Epic. It's like I'm reading the Greeks again.

[Anonymous No.10701432]

>>10701428
What a convincing argument

[Anonymous No.10701438]

>>10701428
Why can't analysts and algebraists just get a long?

[Anonymous No.10701456]

If R' is a subspace of R, and R' has the same dimension as R, how do I prove that R'=R (the book say to show R' "coincides" with R)?

[Anonymous No.10701458]

>>10700079
[math]
\mathbb{W}
\mathbb{H}
\mathbb{Y}\;\;
\mathbb{D}
\mathbb{O}
\mathbb{N}'
\mathbb{T}\;\;
\mathbb{Y}
\mathbb{O}
\mathbb{U}\;\;
\mathbb{T}
\mathbb{R}
\mathbb{Y}\;\;
\mathbb{A}
\mathbb{N}
\mathbb{D}\;\;
\mathbb{F}
\mathbb{I}
\mathbb{N}
\mathbb{D}\;\;
\mathbb{O}
\mathbb{U}
\mathbb{T}
[/math]

[Anonymous No.10701466]

>>10701456
If [math]R=\mathbb{Z}[/math], any nonzero ideal of R has the same "dimension" of R, but is not R.

[Anonymous No.10701481]

>>10701428
wtf i hate group theory now?

[Anonymous No.10701525]

>>10701438
Analysts hate anything that isn't analysis.

[Anonymous No.10701535]

Is the algebra vs. analysis divide actually a thing among mathematicians or is it just retarded undergrads LARPing?

[Anonymous No.10701539]

>>10701535
Take a wild guess.

[Anonymous No.10701559]

>>10701535
Yes and no.
There is a pretty clear bifurcation between analysts and algebraists in most math departments. What you see here is a caricature of that; the real life situation is not
>ME CHAD ANALYST ME NO NEED TO KNOW DEFINITION OF A RING
All analysts use low to mid-level algebra extensively, and all but the most autistic algebraists have fundamental ties to analysis.

[Anonymous No.10701581]

>>10701466
But is Z even a vector space?

[Anonymous No.10701596]

>>10701581
Moreover, does Z even exist? As in truly exist.

[Anonymous No.10701605]

>>10701535
It's literally one fucking guy and we play along for jokes.
>>10701581
>is Z even a vector space
OHHHHH, THAT'S WHY THE QUESTION DIDN'T MAKE ANY SENSE.
Fuck, I was also thinking it was algeo.
Lad, try using the definition of a base.

[Anonymous No.10701612]

>>10701605
>It's literally one fucking guy and we play along for jokes.
It's all me, actually.

[Anonymous No.10701618]

>>10701612
Prove it.
Post the analysis autist's image.

[Anonymous No.10701619]

> Tfw B.A.

how fucked am I

[Anonymous No.10701621]

>>10701618
I'm going to reserve my right to remain silent for this one.

[Anonymous No.10701624]

>>10701619
oh nononono

[Anonymous No.10701625]

>>10701621
The one with a girl offering her hand then pulling it back in disgust.

[Anonymous No.10701640]

>>10698366
should I major in math if I'm not autistic? It's not a passion for me but I like the idea of studying something rigorous.

[Anonymous No.10701644]

>>10701640
Congrats for writing the physically cringiest post I've read this week.

[Anonymous No.10701650]

>hate math
>Everything I want to understand involves math

[Anonymous No.10701651]

>>10701644
what's so cringe about it

[Anonymous No.10701654]

>>10701640
stick to law or psychology bro

[Anonymous No.10701656]

>>10701651
Just interpret it from a non-autistic point of view. Even someone as emotionally disable as you should be able to see why I physically cringed while reading it.

[Anonymous No.10701661]

>>10701654
not interested in either bro

>>10701656
still don't understand

[Anonymous No.10701674]

>>10701640
just go to your library and check out a math book with problems
go at it
then decide

[Anonymous No.10701678]

>>10701212
>Didn't thank me for my latest help vim help
Rude

Anyways, AUCTeX looks pretty neat, but emacs bindings sucks. There's something called evil mode for emacs which emulates vim and it's superior bindings.

[Anonymous No.10701683]

>>10701661
>still don't understand
Put your thinking cap on, or see >>10701654

[Anonymous No.10701721]

>>10701661
>not interested in either bro
I am your rightful ruler. You shall do as I command.

[Anonymous No.10701722]

>>10701651
Part of puzzle: People with an undergraduate in math under their belt is usually past the ((( Rigour ))) meme. It happens to most in their third year when they take analysis.

[Anonymous No.10701848]

>>10701640
>It's not a passion for me
No.

[Anonymous No.10701923]

>>10700476
My school's measure theory course is taught by the toughest prof and I got wrecked hard (the stuff's pretty cool tho)

[Anonymous No.10702004]

>>10701923
measure theory is just very tough in general. lots of pitfalls, ugly arguments with tons of bookkeeping, unintuitive counterexamples, and yucky equivalence classes. it's a very rewarding and fun class once you get to the really nice shit in the end.
it's a class that should wreck you and help you to grow as a mathematician.
now, let's remember our favorite nowhere dense positive measure subset of R!

[Anonymous No.10702037]

I'm sure you goys get this asked a lot. I'm getting back into mathematics and I want some advice how on to path it. I've gone up to calculus at college and I did do well in that class, but I never had a good foundation and I'm thinking about starting back with algebra.

I don't want to meme myself by going through textbooks one at a time and taking a path that may not be necessary. What do you reckon I do? Is there common knowledge of how to study, what to study and what is useless etc? I work in accounting and I don't have too much free time, I don't want to learn what is not necessary to move up or even to just build a core foundation

[Anonymous No.10702077]

>Open textbook
>Chapter 1: 1+1 = 2, we can see this because blah blah
>"man this shit is easy, let's skip to Chapter 2"
>Chapter 2: Given a differential field of Order 2, C, Prove all homomorphisms between R^3 and C are analytic

[http://math.harvard.edu/putnam(...) !!84u21X0KjW+ No.10702151]

Daily Putnam Problem >>10702148

[Anonymous No.10702251]

>>10702037
>What do you reckon I do? Is there common knowledge of how to study, what to study and what is useless etc?

[Anonymous No.10702591]

>>10702077
Yes. And?

[Anonymous No.10702617]

>>10701678
THANK


YOU


The auto-template at startup works. The <++> thing did not. Anyway, I think I can just create a templates folder, open the one I need, and save-as it to the current project.

[Anonymous No.10702718]

>>10702617
> THANK
> YOU
You're welcome :)
>The auto-template at startup works.
Did you get it to work with hotkeys too? Then you can have different hotkeys for different templates from your templates folder not needing to navigate to that folder.
>The <++> thing did not.
Did you try it in insert-mode? I forgot to tell you that it does not work in normal-mode as is (but it's easy to modify it to work in normal-mode as well, or only in normal-mode. Whatever you want.)

[Anonymous No.10702721]

>>10702718
And it's CTRL+(Lower case L)

[Anonymous No.10702744]

>>10702077
(can you see why?)

[Anonymous No.10702786]

>using computers
Ew

[Anonymous No.10702792]

>>10702786
are reading all of the manuscript?

[Anonymous No.10702805]

>>10702718
I had to remove the [math]\mbox{autocmd FileType .tex}[/math] but it worked.

>>10702721
That too.

[Anonymous No.10702813]

>>10702792
I'm browsing books on alg. spaces, stacks and motives to pin down possible research projects.
I'm a bit overwhelmed though. This is stuff that will take a first year of phd to learn. How can I pick enough up to spot out what routes are both feasible and new?

[Anonymous No.10702828]

>>10702805
>I had to remove the "autocmd FileType tex" but it worked.
It does not work in some cases because vim doesn't implement the command before it detect that it is a .tex file. It will work when you create a .tex file by starting vim with "vim filename.tex" or doing ":e filename.tex" inside of vim. If you open an empty buffer, vim does not know that it is a .tex file yet. Removing it more flexible and probably the better solution.
>That too.
Nice

[Anonymous No.10702835]

>>10702805
Forgot one extra thing I have in my .vimrc. Sometimes vim just doesn't detect tex files for some reason. This fixes it.

autocmd BufRead,BufWrite,BufNewFile *.tex set filetype=tex

[Anonymous No.10702836]

>>10699421
>elitist detected

[Anonymous No.10702859]

>>10702835
>Sometimes vim just doesn't detect tex files for some reason.
That was it. ty

[Anonymous No.10702860]

>>10701438
it's a meme, anyone who knows anything about anything knows that math is not sharply divided like this

[Anonymous No.10702878]

>>10702859
Does it paste in on mulitiple openings of the document? Paste your .vimrc? Probably sufficient to remove the "BufRead, BufWrite"

autocmd BufNewFile *.tex set filetype=tex

[Anonymous No.10702880]

Nevermind if you just pressed the binding multiple times.

[Anonymous No.10702918]

>>10702880
Yes, I mashed \tex like a dumb kid. That's how you make science.

[Anonymous No.10703081]

Do you guys know how to solve pic related? I know the derivative of an integral is solved by the TFC, but I can't find how to solve it when is the other way around.

[Anonymous No.10703104]

Is physics just fancy math?

[Anonymous No.10703111]

>>10703104
physics has a completely different goal. math is based on deductive reasoning and physics is empirical. they are logically very different.

[Anonymous No.10703125]

>>10703104
no
math begins from unquestionable axioms
in physics, everything is questionable
theyre totally incompatible

[Anonymous No.10703167]

>>10702744
>>10702591
Feels like I don't have the mathematical maturity necessary to gain mathematical maturity

[Anonymous No.10703361]

lmaoing at this intro book
>section 6.8
Proposition 6.8.11: bla bla
>proof: to prove this, it is easy using the methods of section 7.7, given bla bla and it is proved.
>as a more direct attack, let's use the methods of section 7.6 since they come into play...
>... to obtain the desired objects of Prop 6.8.11, we can use the construction given in the proof of proposition 7.6.4...
>.. we can conclude from proposition 7.6.5 that ...

like has the author forgotten it's an earlier chapter?
Regardless, the book is still great (and also the proof).

[Anonymous No.10703379]

>>10703361
>lmaoing
>lauging my ass offing
What?

[Anonymous No.10703382]

>>10703379
thats right

[Anonymous No.10703391]

Tell me the fifth Ramsey number!
I give you 20 minutes

[Anonymous No.10703460]

>>10703361
Best case: It was a sacrifice to make the progression clearer in some other way and it worked.
Other cases: There are many of them, and they are worse.

[Anonymous No.10703483]

>>10703391
At least he's only asking for the number and not any reasoning. Just guess, you have a 1/6 shot at not dying

[Anonymous No.10703498]

>>10703483
1/7, or did I miss a new estimate?

[Anonymous No.10703701]

>>10703483
Nice, it's Russian Roulette.

[Anonymous No.10703872]

http://www.kurims.kyoto-u.ac.jp/~motizuki/news-english.html
>2019-06-07
>(Papers) Updated comments concerning: Topics in Absolute Anabelian Geometry III.
>(Papers) Revised version (list of revisions): Inter-universal Teichmuller Theory III: Canonical Splittings of the Log-theta-lattice.

http://www.kurims.kyoto-u.ac.jp/~motizuki/2019-06-05-iu-teich-iii-revisions.txt
>Added Remark 2.4.2
>Corrected misprints in the statement of Proposition 3.9, (i) ("compact open subsets" ---> "nonempty compact open subsets", "compact closures of open subsets" ---> "compact closures of nonempty open subsets")
>Added Remark 3.9.7
>Added Remark 3.10.2
>Modified the final portion of Remark 3.11.1, (ii)
>Modified the discussion of "IPL" in Remark 3.11.1, (iii)
>Modified the final portion of Remark 3.11.1, (iii), and added a related reference to [IUTchII], Remark 1.9.2, to Remark 3.11.1, (iv)
>Modified the first paragraph of the proof of Corollary 3.12, and added a reference to this first paragraph to the discussion immediately following the first display of Step (xi-b), as well as to the discussion immediately following the second display of Step (xi-d)
>Slightly modified the wording (deleted the word "arbitrary") of the third display of Remark 3.12.2, (v)

http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20III.pdf

[Anonymous No.10703879]

>>10698366
>x+0=0
immediately closed this book, tore it apart, and tossed it in the fireplace.

[Anonymous No.10703880]

>>10703498
Depends what you mean by new. The current range is 43-48. According to Wikipedia the lower bound is fairly old but the upper bound was bumped down to 48 in 2017.

[Anonymous No.10703916]

>>10703879
It's true though. [math]x + x = x[/math] also follows if [math]x \in \mathbb{Z}[/math].

[Anonymous No.10703953]

>>10703081
Fundamental Theorem of Calculus works here just as you would expect

[Anonymous No.10703986]

>>10703872
Why won't brainlets admit he's right?

[Anonymous No.10704414]

>>10702037
read aluffi's algebra chapter zero, it's a soft and low prerequisites ease back into your typical introductory algebra. you should be able to find pdfs online! remember to do the odd exercises.

[Anonymous No.10704416]

>>10703081
the fundamental theorem of calculus has two parts. look at the other part.
if that's not enough, here's another hint. what is the antiderivative of the derivative of sqrt(t^2 + 8t + 1)?

[Anonymous No.10704645]

>>10698937
*laughs in Mathematical Physicist*

[Anonymous No.10704659]

>>10703872
mochiman did it and people are too afraid to admit it

[Anonymous No.10704740]

>>10703986
They don't watch enough anime (or other weeb media) to actually understand on an intuitive level how his Jap mind operates.

[Anonymous No.10704830]

Ive been building something with distance sensors and I ran into a trilateration problem.
getting 1 of the dimensions is easy, but the third one is a pain, Essentially I have two know distances say r1, and r2, from points (a,0) and (0,b) respectively. Ive solved it using trilateration and the solution is horribly ugly and hardly anything falls out of the algebra. Ive also solved it using trilateration and it gave a much simpler solution but it still feels like its too complicated. Has anyone seen an elegant solution to what I would think would be a common trilateration problem. If I didnt need this to run in code Id use transformation matrices.

[Anonymous No.10704832]

>>10704830

[Anonymous No.10704991]

>>10703880
Yeah, that's it. I only remembered 43-49

[Anonymous No.10705012]

>>10704830
>If I didnt need this to run in code Id use transformation matrices.
Why does having to run it in code exclude you from using transformation matrices?

At worst type it into a CAS and use the simplification.

[Anonymous No.10705016]

>>10703125
>math begins from unquestionable axioms
Factually incorrect. The Axioms HAVE been questioned many, many times.

[Anonymous No.10705023]

>>10700544
I suspect the white man writes his own text editor, but I really do not have the time to do that.
Also both vi and emacs are amerimut software.

[Anonymous No.10705090]

>>10705012
Sorry I didn't make that clear at all. Its running on a microprocessor to handle the sensors. So it won't have much computational power.

[Anonymous No.10705094]

>>10705090
Yeah, that is what I suspected, but:
-Are transformation matrices really that slow?
-Can't you formulate the solution with transformation matrices and ask a CAS to simplify?

[Anonymous No.10705257]

What do i read if i want to get into matroid theory?

[Anonymous No.10705274]

I applied to a master program that has paths for both pure and applied math, but most researchers there seem to lean foward the applied part.
Did I fucked it up if I prefer pure?

[Anonymous No.10705322]

>>10703872
>http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20III.pdf
>Most of the references are to his own works
>Only exceptions are basic graduate texts

He is just a more succesful wildberger.

[Anonymous No.10705386]

>>10705322
>[Lang] S. Lang, Algebraic number theory, Addison-Wesley Publishing Co. (1970).
Lang is a meme.

[Anonymous No.10705388]

>>10703125
>unquestionable axioms
come back after you watch some wildberger kid

[Anonymous No.10705407]

whats 6+8

[Anonymous No.10705411]

>>10705407
What have you tried?

[Anonymous No.10705420]

>>10705411
my calculator crashed thats why im here

[Anonymous No.10705421]

>>10705407
7+7
8+6
9+5
10+4
11+3
12+2
13+1
14
By repeated applications of the Peano axioms.

[Anonymous No.10705426]

>>10705407
[math]6\amalg_{\emptyset} 8[/math]

[Anonymous No.10705440]

>>10705421
>>10705426
well i dont see how that would be logical but im gonna take your word for it

[Anonymous No.10705470]

>>10705322

Why do people think it's OK to criticize Mochizuki without even understanding his proof?

There was one time last year when my analysis TA gave me a bad grade on a quiz reflection we had to write. On the quiz, there was a very trivial theorem we had to prove and I lost a bunch of points on that question even though I was confident that I was right. In the reflection, I tried to refute his grading based on purely technical reasons arguing that my proof was correct.

On my graded reflection, he argued that I lost points because it was too hard to understand. He actually compared my proof to Mochizuki's proof of the ABC conjecture, saying it was useless because nobody understands it.

Mochizuki isn't a crank, he's a professor at a respected institution. He worked for years on a very hard problem and now he thinks he has solved it. He's not an example of what not to do. In fact, you and me are mere buffoons not fit to hold the petticoat of the Master.

[Anonymous No.10705524]

Is statistics the most boring branch of math?

[Anonymous No.10705744]

>>10698366
Brainlet here, I need help working something out. Multiple choice answer
>A and B are numbers. How many times greater than the average of ½ A and ½ B is the average of 4A and 4B?
the answer is between:
>4
>6
>8
>1/2
what is it, and more importantly, why? I have no idea what the fuck it's talking about

[Anonymous No.10705779]

the average of two numbers can be is a function [math]f(a,b)=\frac{a+b}{2}.[/math]

Notice that if we multiply a and b by the same thing, we can just factor it out of the sum in the numerator.

So, [math]f(ka,kb)=kf(a,b).[/math]


[math]\frac{f(4a,4b)}{f(\frac{1}{2}a,\frac{1}{2}b)}=\frac{\frac{1}{2}f(a,b)}{4f(a,b)} =8[/math]

[Anonymous No.10705834]

>>10705388
if you question choice youre in the wrong profession faggot

[Anonymous No.10705888]

>>10705779
I still don't get it, but thanks anyway

[Anonymous No.10706003]

>>10705470
you must have been really awful at analysis to write an undergraduate quiz proof in a way that is remotely difficult to understand for a graduate student.
for that reason, i choose not to agree with your likely incorrect opinion.

[Anonymous No.10706011]

>>10705834
if you don't question the well ordering theorem when you first hear of it, you're the one in the wrong profession. think for yourself instead of listening to what everyone tells you.

[Anonymous No.10706169]

>>10705744
The average of 4A and 4B is (4A+4B)/2=2A+2B=2(A+B).
The average of (1/2)A and (1/2)B is ((1/2)A+(1/2)B)/2=(1/4)A+(1/4)B=(1/4)(A+B).
2(A+B) / (1/4)(A+B) = 2/(1/4) = 8.
IOW, the average of 4A and 4B is 8 times the average of (1/2)A and (1/2)B.

[Anonymous No.10706774]

>>10706011

[Anonymous No.10707011]

>>10705888
Think of the function that he mentioned as a bijection from [math]\mathbb{R} \rightarrow \mathbb{R}[/math]. This function is a holomorphic mapping on the Complex Riemannian sphere which can be proved in a few lines. Next you need to show recite what I just said in front of the bathroom mirror with the lights off 3 times, and then you just need to use some elementary algebraic topology to prove that $[math]\mathbb{R}[/math] is null homolygous

[Anonymous No.10707104]

>>10706011
>my favorite context of choice is hard on my brain owwie
fuck you retard
every surjective function is right cancellative

[Anonymous No.10707242]

>>10707104
Describe for me the maximal ideal in the countable direct product of Z which contains the countable direct sum of Z.
Please enlighten me as to the nature of a vector basis for R as a space over Q.

[Anonymous No.10707247]

>>10707104
>>10707242
To be clear, I do believe wholeheartedly that all these things are true and exist. I just don't think saying "AoC is obvious to anyone with a brain" is very instructive when there are so many ridiculously unintuitive immediate corollaries of even just Zorn's lemma (which seems pretty obvious in its own form to begin with).

[Anonymous No.10707363]

>>10707247
i think its wrong to question an axiom when it leads to things that are hard to think about, thats backwards
you determine consequences from axioms, you dont change axioms to get the "right" consequences

choice has things that its equivalent to, like a product of non empty sets is non empty
and any one of those obvious equivalents its enough to take choice as an axiom

i think this is more a problem of existence proofs in general than of choice
i can prove that there are infinitely many primes, but i cant give you any nth prime, at least not in a reasonable amount of time

[Anonymous No.10707604]

>>10698366
I'm bad at maths.
the monkey in my brain starts throwing things once i get past trig.

[Anonymous No.10707606]

>>10698873
points along its circumference, or just in general?

[Anonymous No.10707609]

>>10698873
also, what does pie look like outside of base 10?

[Anonymous No.10707726]

>>10707609
wait.. could you.. could you make a numeric system in base pie?

[Anonymous No.10707897]

Please... somebody... I need those problem sheets. /sci/ recommended me this guy a while ago and I love the way he teaches, but I need those problems sheets to make it an effective way to study

https://www.youtube.com/playlist?list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic

[Anonymous No.10707902]

>>10707897
I don't help fr*gposting garbage, sorry.

[Anonymous No.10707973]

>>10698937
when would mathematicians ever have to work with feynman diagrams

[Anonymous No.10707988]

>>10707973
B-but category theory has diagrams!!!!

[Anonymous No.10708012]

How do you manage the stress from staring at hieroglyphics all day? Just opening a .pdf makes me nervous. Also, my eyeballs are hurting.

[Anonymous No.10708215]

>>10708012
they're not hieroglyphics if you can read them fluently

[Anonymous No.10708223]

>>10708215
I can read them. That's not the point.

[Anonymous No.10708253]

how far can I get into math learning through wilderberger's foundation classes? it's so comfy it makes me want to learn

[Anonymous No.10708262]

>>10708012
>How do you manage the stress from staring at hieroglyphics all day?
Because I actually enjoy reading manga. I don't see how that's relevant to opening .pdfs and studying math though.

[Anonymous No.10708272]

>>10708253
He is teaching pretty much nonstandard mathematics, so "how far" doesn't really make sense, as the measure of "how far" has to be based upon standard mathematics.

[Anonymous No.10708295]

>>10708253
you really really should not do that

[Anonymous No.10708322]

How do I manage the relaxation/study balance?
I want to study things on my own but activities like videogames and manga have a but disappeared for me. I don't know how to study math while not drowning myself in exercises, desu

[Anonymous No.10708329]

>>10708322
just schedule the time you spend on math

[Anonymous No.10708370]

Does higher level math actually help solve equations in physics (PDEs especially) or are spectral methods and fea all we have?

[Anonymous No.10708445]

...the thing is that anxiety comes from perceived inadequacy; and since research is about "exploring the unknown", anxiety never really leaves you

[Anonymous No.10708476]

>>10708445
I can't wait for my PhD studies to start. I'll be crushed by that anxiety by then, and then I can go shake my advisor's hand and say good bye before even starting.

[Anonymous No.10708479]

When would you consider someone a good mathematician?

[Anonymous No.10708484]

>>10700710
I want to know everything!!! Lol.
Bought 900 pages of algebra ...

[Anonymous No.10708498]

>>10708476
>I can't wait for my PhD studies to start.
Me too. There's a point where the anxiety plus the abstractedness of thought push you into a kind of extracorporeal experiencd which is better than any drug. I remember having anxiety crisis in early high school, and once I woke up in the middle of the night in a sort of semi-conscious nightmare where I thought I was at school being asked Brain-Training-style math questions & trivia along with questions about the Iliad and the books I could not get to read in time for lit class, until I finally realised I was allowed to rise and go to the bathroom.

[Anonymous No.10708521]

>>10708479
When they stop feeling the need to ask retarded questions on a Chinese BBS.

[Anonymous No.10708525]

>>10708521
There are a lot of mathematicians out there then, even a lot of ones who don't even do mathematics...

[Anonymous No.10708533]

I can't multiply two three-digit numbers in my head without forgeting the previous steps lmao

[Anonymous No.10708738]

>>10708533
I can't multiply two arbitrary two-digit numbers in my head. You don't need that.

[Anonymous No.10708795]

What's currently HOT in algebraic geometry?

[Anonymous No.10708833]

>>10708795
>algebraic geometry
dead field

[Anonymous No.10708855]

>>10708012
>Also, my eyeballs are hurting.

Get an e-reader big an A4 screen size. ie Sony DPT

[Anonymous No.10708878]

>>10699380
>Everyone said calc 3 is easier than calc 2...


Everyone didn't say that. Also Calc 3 is easy so man up.

[Anonymous No.10708881]

>>10699380
What are you having trouble with?

[Anonymous No.10708903]

>>10708795
CM abelian varieties

[Anonymous No.10708936]

Hello friends. Complex analysis question.

I'm having a real hard time understanding the Mittag-Leffler and Weierstrass Factorization theorems in complex analysis. There aren't many resources about these things (besides grad level books that are above my mathematical maturity) and the theorems I've read only only concern uniqueness (especially with mittag leffler) but not actually how to construct such a function. There's the series of partial fractions, but is it really just as simple as defining a series of partial fractions with poles (counting multiplicity) and then proving this series converges on every compact set in C or is there something I am 'missing'?

As far as weierstrass factorization, is the holomorphic function in the exponent unique for each given sequence of weierstrass elementary factors and multiplicity of zeroes (I would think so?)?

[Anonymous No.10708940]

>>10708936
*compact set in c punctured at its poles, sorry

[Anonymous No.10709041]

>>10708936
>Weierstrass
We take an entire function, and we break it up into a simple enough function with the appropriate zeroes, and a function that's never zero. We need to give it's zeroes at 0 separately since E doesn't fucking work. The only part of the proof you need to actually concern yourself with is "can we write any function that never zeroes as e^g(z)?".

[Anonymous No.10709463]

What would a synthetic approach to group theory look like? What would be the definitions and postulates?

[Anonymous No.10709471]

>>10709463
Is your pic related?
In any case, if I take the common notion of "syntetic" vs. "analytic" that I have in mind, I'd say the normal group theory axioms are already primitive and syntetic.

[Anonymous No.10709496]

>>10709463
Group theory is already synthetic.
Analytic group theory would be taking a group to be a subgroup of the group of automorphisms of some set.

[Anonymous No.10709504]

Anyone here into derived categories, stacks, dg enhancments? What's some accessible open problem to tackle?

[Anonymous No.10709523]

>>10709496
Nevermind.
You can consider an element to be a point, and the subgroup generated by it to be a line. Similarly, the subgroups generated by two elements become planes, and so on. Essentially, completely forget multiplication and consider the spans of elements.
Should work for finite groups, but skew off from classical group theory on infinite ones.

[Anonymous No.10709608]

>>10709504
>What's some accessible open problem to tackle?
What have you tried?

[Anonymous No.10709616]

>>10707973
https://arxiv.org/abs/hep-th/9912092
https://arxiv.org/abs/1006.4064
https://www.math.toronto.edu/drorbn/papers/weights/weights.pdf
https://arxiv.org/abs/1108.3103

[Anonymous No.10709620]

>>10709616
>drorbn
literal hack

[Anonymous No.10709624]

>>10709620
>made significant progress towards Kashiwara-Vergne
>hack
??

[Anonymous No.10709631]

>>10709523
I'll add onto this.
Let G be a set. We call a group structure on G a map g from P(G)\empty to P(G) such that:
>[math]A \in g(A)[/math]
>g is idempotent
>A contained in B implies g(A) contained in g(B)
So g is a closure.
>if A is an infinite set, g(A) is the union of all g(B), where the union goes through all finite B contained in A
If we don't include this, we consider the possibility of multiplying an infinite amount of terms. Which might be interesting, but completely fucks up any possibility of a constructive proof for the infinite case.
>the intersection between every g(A) is equal to {0}
Most likely unnecessary, but kept just in case.

We can send a group to a group structure by taking subgroups, and a monoid (or semigroup, removing the last axiom) by taking submonoids (or subsemigrous).
I don't feel arsed to even try to give a constructive proof that we can send a group structure to an appropriate semigroup at this time of the night. If I come up with something I'll post it some other day.

[Anonymous No.10709641]

>>10709631
Fuck, I forgot, but we need to include Lagrange's theorem as an axiom.

[Anonymous No.10709648]

>>10709624
>le angry neurotic jewish manlet
it's like he's desperately trying to be a stereotypical woody allen character

[Anonymous No.10709651]

>>10709641
Nope, can't guarantee the existence of adequate subgroups unless I stack axioms upon axioms. Forget it.
I'll go to sleep now.

[Anonymous No.10709663]

>>10709648
Well yeah he called me a retard once but that doesn't make him a hack

[Anonymous No.10709728]

https://terrytao.wordpress.com/2019/06/08/ruling-out-polynomial-bijections-over-the-rationals-via-bombieri-lang/
>I recently came across this question on MathOverflow asking if there are any polynomials P of two variables with rational coefficients, such that the map P: Q x Q -> Q is a bijection. The answer to this question is almost surely “no”, but it is remarkable how hard this problem resists any attempt at rigorous proof. (MathOverflow users with enough privileges to see deleted answers will find that there are no fewer than seventeen deleted attempts at a proof in response to this question!)

>On the other hand, the one surviving response to the question does point out this paper of Poonen which shows that assuming a powerful conjecture in Diophantine geometry known as the Bombieri-Lang conjecture (discussed in this previous post), it is at least possible to exhibit polynomials P: Q x Q -> Q which are injective.

>I believe that it should be possible to also rule out the existence of bijective polynomials P: Q x Q -> Q if one assumes the Bombieri-Lang conjecture, and have sketched out a strategy to do so, but filling in the gaps requires a fair bit more algebraic geometry than I am capable of. So as a sort of experiment, I would like to see if a rigorous implication of this form (similarly to the rigorous implication of the Erdos-Ulam conjecture from the Bombieri-Lang conjecture in my previous post) can be crowdsourced, in the spirit of the polymath projects (though I feel that this particular problem should be significantly quicker to resolve than a typical such project).

[Anonymous No.10709788]

>>10701226
that shit looks like it was taken from IUTT

[Anonymous No.10709816]

>>10709663
>he called me a retard once
To be fair, most people you know probably did too, just not to your face.

[Anonymous No.10709822]

>>10709728
Cool.

[Anonymous No.10709891]

Consider the domain in pic related and the following equations.
[eqn]
\begin{align}
\partial_t u - \nabla \cdot (\beta \nabla u) &= f &&\text{in } \Omega_1 \cup \Omega_2 \\
u &= g &&\text{on } \partial\Omega \\
\left[u\right] &= a &&\text{on } \Gamma_\text{I} \\
\left[\beta \nabla u \cdot \mathbf{n} \right] &= b &&\text{on } \Gamma_\text{I}
\end{align}
[/eqn]
where [eqn]\left[v\right](\mathbf{\gamma}) = \left(\lim_{\mathbf{x}\to\mathbf{\gamma} \land \mathbf{x} \in \Omega_1} v(\mathbf{x}) \right)- \left(\lim_{\mathbf{x}\to\mathbf{\gamma} \land \mathbf{x} \in \Omega_2} v(\mathbf{x})\right)
[/eqn]
Basically this models functions with discontinuities along some irregular interface that partitions the domain. This is known as a parabolic interface problem if you want to look into some of the literature.

I'm trying to use this to model passive and active diffusion across a cellular membrane but can't figure out what kind of conditions to impose on [math]a[/math] and [math]b[/math] to get it to feel natural. All the papers I've looked into kind of decouple the interface conditions from the rest of the system too much (e.g. https://doi.org/10.1002/cnm.1132 ). I'd like to get things like Nernst potentials to show up properly. I know this is a niche topic but any ideas on how to proceed?

[Anonymous No.10709892]

>>10707363
>at least not in a reasonable amount of time
but you can conceive of a way to do so, while i provably cannot conceive of a way to construct a maximal ideal in the countable direct product of Z containing the countable direct sum of Z.
i agree with your objection against questioning an axiom. however, it is easy enough to understand why someone would reject something that causes nonconstructable consequences, just as we reject the axioms of naive set theory because they cause paradoxes. one could very easily decide that "this thing exists but cannot be exhibited" is a paradox under the right logical framework. we don't do that, but there are people who do.

[Anonymous No.10709893]

Will knowing calculus help me understand statistics? I fucking hate statistics. I feel like it's just a bunch of formulas that I have to memorize.

[Anonymous No.10709898]

>>10709893
yes
statistics is calculus

[Anonymous No.10709909]

>>10709898
I shouldn't have taken this before calc then. No wonder I started feeling like I was just plugging things in after the first few chapters. Why isn't calc a prereq for stats?

[Anonymous No.10709922]

>>10709909
because stats is usually not taught with calc and most people who are taking stats dont want to have to take calc
you need to take a calculus based statistics class if you want to understand statistics

[Anonymous No.10709956]

>>10709922
Alright, thanks. I guess I'll stop worrying about understanding for now and just focus on memorizing the procedures.

[Anonymous No.10709958]

>>10709956
>I'll stop worrying about understanding
Yep, sounds about right for anything involving "calculus".

[Anonymous No.10710466]

>>10709616
Posting Witten isn't fair, Kontsevich and Khovanov on the other hand.

[Anonymous No.10710481]

>>10708533
If only there was a simple algorithm that would let me easily write down each step of such calculations... Oh well, a man can dream, amirite?

[Anonymous No.10710524]

What is the Witten genus?

[Anonymous No.10710592]

>>10708795
. rational points on varieties
. mirror symmetry
. enumerative geometry and invariant theory (moduli theory, gromov-witten theory, and others)
. motivic decompositions of varieties
. Hodge conjecture
. and probably more I am forgetting

on the arithmetic side:
. p-adic cohomology of p-adic varieties
. Arakelov geometry
. more rational points
. BSD conjecture
. and more I don’t know

[Anonymous No.10710624]

>>10709631
>>10709496
What I meant by synthetic is that it isn't formulated in terms of some other theory. The group axioms are stated in terms of a set and a function between sets, so group theory is "analysed" through set theory. Similarly analytic geometry uses the reals to analyse geometry, whereas synthetic Euclidean geometry doesn't make use anything external to itself.
https://golem.ph.utexas.edu/category/2015/02/introduction_to_synthetic_math.html
>>10709471
Pic not related.

[Anonymous No.10710705]

>>10709608
I've tried to read the important literature before the application deadline, but it's thousands of pages and I'm stuck. Please help. Am I just supposed to ask to one of the possible advisors?

[Anonymous No.10710724]

>>10700079
Function and series is probably the easiest and most applicable of those.
That, or basic number theory. The other three are more "abstract", although in my opinion, group theory is easier than Analysis on manifolds and Measure and integration.

[Anonymous No.10710944]

>>10710724
an introductory group theory class is objectively easier than either an analysis on manifolds class or a measure theory class.

[Anonymous No.10711030]

How do we save differential topology?

[Anonymous No.10711066]

>>10710944
It depends on the uni too ofcourse. At my uni the group theory class is harder than the measure theory class

[Anonymous No.10711200]

>>10709728

That's actually interesting

[Anonymous No.10711208]

>>10710624
>dodging set theory to formulate group theory
Undoable. You can abstract away a lot, such as the function on two arguments defining multiplication, but you ultimately can't get away from the axiom schema of specification unless you want to define things like "span", "normal subrgoups", "the center of the group" or various other notions.That's enough reason to ground it in set theory.
You'd need some wildly, unimaginably autistic approach.

[Anonymous No.10711222]

>>10711208
>You'd need some wildly, unimaginably autistic approach.
Indeed

[Anonymous No.10711225]

What's a way to explain in a formal letter that I was able to prove a small original result in my MSc thesis without boasting like a pretentious asshole or sounding like a total nincompoop.

[Anonymous No.10711226]

>>10705744
1/2 = 0.5
8 * 0.5 = 4

Simpler still 8*(1/2) = 8/2 = 4

Also
1/2A + 1/2B = 1/2(A + B)

[Anonymous No.10711227]

>>10711225
>While inspired by the likes of Mochizuki, Wiles and Grothendieck, I was able to prove on my own this minor result...

[Anonymous No.10711229]

>>10711208
>Undoable.
I assume the proof is left to the reader?

[Anonymous No.10711230]

>>10708479
Studied 5000+ hours
E.g. Bachelors + Masters in maths

[Anonymous No.10711238]

>>10711222
>you literally need to specify that it has finite products and a final object
>based on category theory
>axioms are low key longer then the classical ones
It's shit.
>>10711229
It isn't literally undoable, you'd just need something as strong as the axiom schema to show that the center subgroup exists, along similar statements. And if you're already building that up, there isn't a point not to just build set theory, and then build group theory on top again.

[Anonymous No.10711241]

>>10711225
List the spin-off paper where you published this result in your [published works] section. If you did not publish it in a spin-off paper, then it isn't relevant enough to boast about.

[Anonymous No.10711242]

>>based on category theory
As anything self-respecting should be these days.

[Anonymous No.10711245]

>>10711238
>you literally need to specify that it has finite products and a final object
>axioms are low key longer then the classical ones
>it's shit
Retard detected.

[Anonymous No.10711277]

>>10711241
>If you did not publish it in a spin-off paper, then it isn't relevant enough to boast about.

[Anonymous No.10711311]

>>10705744

what's the intuitive solution for this? I feel like solving things through algebraic manipulations a bit hacky

[Anonymous No.10711313]

>>10711208
>the function on two arguments defining multiplication
>abstract away a lot

[Anonymous No.10711325]

>>10708878
I've been saying that

[Anonymous No.10711333]

>>10711313
Picture matroids, except for groups.

[Anonymous No.10711348]

>>10699440
>learning math "historically" is just you procrastinating from actually learning math
Based

[Anonymous No.10711369]

>>10711277
Don't be sad. I'm sure it's worth at least something if you posted such a cute picture.

[Anonymous No.10711374]

what is your favourite number theory proof?

[Anonymous No.10711379]

>>10711374
proof that 1+1 is convergent

[Anonymous No.10711382]

>>10711374
proof that 1+1=2 and not infinity.

[Anonymous No.10711391]

>>10711379
>>10711382

very funny

for me, it's the proof the reals don't exist

[Anonymous No.10711393]

Taking elementary analysis this fall, what am I in for?

[Anonymous No.10711402]

>>10711374

Lagrange's four square theorem is good too.

[Anonymous No.10711407]

>>10711311
The average of 1/2 A and 1/2 B is just half the average of A and B. Same for 4A and 4B, just 4 times the average of A and B. From there it's clear that one is 8 times the other.

[Anonymous No.10711416]

>>10711393

It's really lame.

They will throw the book at you over any minor fuckups on quizzes, tests and assignments because they think undergrads are short bus tards who need this since they were expecting "superimposed fibonacci spiral" numerology bullshit

[Anonymous No.10711424]

>>10711416
I did well in Diffeq and linear algebra, so will this be a cakewalk

[Anonymous No.10711429]

>>10711416
undergrads are short bus subs tho

[Anonymous No.10711431]

>"A career as a lawyer was planned out for Lagrange by his father, and certainly Lagrange seems to have accepted this willingly. He studied at the University of Turin and his favourite subject was classical Latin. At first he had no great enthusiasm for mathematics, finding Greek geometry rather dull. It was not until he was seventeen that he showed any taste for mathematics – his interest in the subject being first excited by a paper by Edmond Halley which he came across by accident. Alone and unaided he threw himself into mathematical studies; at the end of a year's incessant toil he was already an accomplished mathematician. "

IQ is hardest pill to swallow

[Anonymous No.10711435]

>>10709956
not going to make it

[Anonymous No.10711453]

>>10711429
>>10711431

i was doing shit like ramsey theory and abstract algebra in highschool

[Anonymous No.10711501]

>>10711030
Apply it to comp sci, biology, and physics, not because you want to, but because that's where the grant money is at.
>>10711225
>>10711241
>>10711277
If you didn't have enough material to publish a new paper based on the result you could instead talk about the work in the context of developing it enough to actually publish a paper. I'd say something like "during the course of my master's thesis I was able to extend [insert result], my plan is to build on this result [in X direction] and submit it for publication later on." People forget that a lot of original work does contain steps that on there own are just "minor" results, but many of those chained together can lead to major results.
>>10711374
Quadratic reciprocity

[Anonymous No.10711516]

>>10711501
>Quadratic reciprocity
Which proof?

[Anonymous No.10711537]

>>10711393
only good undergrad introductory class
>>10711374
number theory is not mathematics. number theorists do not do proofs in the truest sense of the word.

[Anonymous No.10711565]

>>10711537
>number theorists do not do proofs in the truest sense of the word
Why not?

[Anonymous No.10711575]

>>10711537

> number theory is not mathematics. number theorists do not do proofs in the truest sense of the word.

OKAY BUDDY

[Anonymous No.10711591]

>>10711565
>>10711575
seething number theorist tards. you people truly are pathetic. number theory is not mathematics, it is trickery and games. analytic number theory is the truest bastardization of the beautiful and elegant world of analysis. utterly disgusting. number theorists are like the heretics of the church of mathematics (and algebraists are the heathens). go fuck yourself you fucking pieces of shit.

[Anonymous No.10711595]

Does the inverse function theorem go both ways? So I want to know wether for all functions f : R^n -> R^m and all points x in R^n, if there exists a neighbourhood of x such that f is locally invertible, then f'(x) is invertible.

[Anonymous No.10711598]

>s*ething number theorist tards.
I'm not even close to being a number theorist. I just asked "why not" and you failed to reply.
>beautiful and elegant world of analysis
Oh, I see... I'm really sorry to hear about condition, anon.

[Anonymous No.10711604]

>>10711595
could you possibly think for 5 seconds about your problem before asking others?
what about the fucking identity function? lmao

[Anonymous No.10711610]

>>10711598
you're probably a fucking alg geo autist or something, especially considering the reddit quality of your post. whatever. it's all the same to me, you are probably masturbating pathetically probably using a prostate stimulator with your stupid fucking diagrams and structures while i engage in the timeless art of bounding and limiting.

[Anonymous No.10711623]

>>10711604
The identity function doesn't contradict anything though... let f : R^n -> R^n be the identity function, then for all x you have that f'(x) is the identity matrix, which is always invertible, just like how the identity function is invertible.

[Anonymous No.10711629]

>timeless art of bounding and limiting.
I hope you get well soon, anon... I hope your family is there for you right now.

[Anonymous No.10711640]

>>10711416
Undergrads are retards

[Anonymous No.10711653]

>>10711595
There are counter examples in f: R -> R. A globally invertible function can have points with zero derivative. It could also have points where it isn't differentiable.

[Anonymous No.10711658]

what will the analyst ITT do if you cypher his furry porn? just will prime numbers into nonxistence?

[Anonymous No.10711671]

>>10711516
Eisenstein

[Anonymous No.10711680]

Hey, lad who's been alternating making these threads with me.
Wanna make the next one?
>>10711595
Could you not call Jacobi's matrix f'?
Also, no. Consider f(x)=x^3 from R to R.

[Anonymous No.10711756]

>>10711629
how fucking new do you have to be to not understand how to reply to someone
are you some kind of idiot?

[Anonymous No.10711763]

>>10711658
i'll go find it again on e621, they probably have more decorum over there than fucking numby cuckles do

[Anonymous No.10711890]

>how fucking new do you have to be to not understand how to reply to someone
>are you some kind of idiot?
how fucking new do you have to be to not understand that some users of this forum don't deserve any (you)'s
are you some kind of idiot?

[Anonymous No.10712141]

>>10699440
>>10699388
I'm gonna second the reply to this. Math is completely different from how it was just 80 years ago. Do not start from the beginning.

[Anonymous No.10712182]

>>10711890
oh so it's a petty thing
fine, continue being petty. i don't have time for people who don't respect analysis.