/mg/ - maths general

[Anonymous No.10946255]

Previously >>10930547
Top Vect edition.

[Anonymous No.10946533]

the /mg/ is dead
long live the /mg/

[Anonymous No.10946711]

I have a quiet week and will try out new things. Does anybody want to do a video interview about their work or math in general? Write me.

>>10946255
I have a fascination with fixed point theorems, but I didn't find this one fat springer book (of the name Fixed Point Theory, I think), very accessible.
On a related note, topologies kind of make me uneasy - or rather the fact that we can assign various topologies for a space and derive various things. How to know what topologies to consider or what we are missing out because we haven't some yet? Frustrating.

[Anonymous No.10946723]

>>10946711
Try Zeidler's nonlinear functional analysis, the first volume is about fixed point theorems.

[Anonymous No.10946749]

>>10946711
If you have two topological spaces with the same underlying set, don't think of them as the same set with different topologies. think of them as two completely different spaces that just happen to have elements with same name.

[Anonymous No.10946774]

>>10946723
Ah okay, will take a look. I a really at one point bought the first 2500 pages of his love child book series. It's a bit of a meme as far as textbooks go, but I still really like it.

>>10946749
Fair enough!
Okay let me row back and make the statement a bit differently: With topology it feels like we could apply miss something more or less simple and that's frustrating. The non-obvious topologies that were established and researched later still have strong use and that fact alone makes it feel like we can't exhaust it even with clever people and a lot of work. I know some may actually like that, though.

Again, call is open for a hot take I would publish, on some STEM stuff.

[Anonymous No.10946815]

>>10940305
Apology for the late answer, but I can't really help, most of the Algebra I learnt is from books that haven't been translated.
I think getting a little bit of mathematical maturity is useful. Maybe "Algebra: Chapter 0" is better, idk.

>>10946711
>>10946774
>topologies
I don't think it's frustrating, I think it leaves the space you're considering open for further studies, leaves more tools to be invented.
Interesting book, a shame that I like physical versions of textbooks and I'm poor as fuck right now. Kinda wish mathematicians and physicists would talk more, I feel the two disciplines have become so speicialised nobody bother to learn about what's happening on the other.

[Anonymous No.10946831]

>>10946815
>Kinda wish mathematicians and physicists would talk more, I feel the two disciplines have become so speicialised nobody bother to learn about what's happening on the other.

But last 30 years mathematics has been lead by String and Quantum Field theories.

[Anonymous No.10946841]

what's your studying/note-taking workflow like?

>blog
I'm always bouncing around with different methods yet always still suffering from being unorganized and inoptimal, having either a) heaps of unorganized chicken scratch or b) confusing notes spread sporadically throughout my laptop. And if I try to use my computer too much I start to hate my life and math gets real uncomfy. If I don't use it all I just give up on trying to redeem piles of chicken scratch that would otherwise be valuable.

I'm going to try going back to basics and just using one composition notebook per book (well, more than one if it's a thicc book), wherein i keep well written notes and attemps at solutions to problems. I don't really take many notes, fwiw, mostly just spend the time solving, and reviewing problems/proofs. For those hairy problems that span multiple pages of scratch work, I will refine it after completion and rip out the chicken scratch afterwards but still leave a breadcrumb trail as to how i found the solution. It helps that it's already bound together, small and aesthetic af.

So this doesn't get unweildy I will be using org mode for end of day transcriptions to the pc so shit's searchable and stored neatly forever if appropriate (using org-noter/interleave so my notes to correspond with page numbers on a pdf for easy cross-file linking), and will be setting up org-drill so it cycles through problems/proofs I had difficulty with so i can review them. External links and references (often saving a stack exchange link helps when looking back on a problem) can be handled with org-ref and helm-bibtex.

wish me luck, i just wanna be comfy. pls give tips

[Anonymous No.10946851]

>>10946841
I keep printer paper at my desk for hairy problems that I want some room to work through. A chalkboard would be far more aesthetic, even a whiteboard would be nicer, but hey.

[Anonymous No.10946865]

>>10946815
It's meme series in that it's 4000 pages of him going through his favourite math topics and brings up how they are needed for physics. But it's not logically threaded in particular. It only works inasfar you basically can use everything in mathematical comprehension, in some way, to study QFT. He has some rather nonstandard (for a textbook on QFT) notes on combinatorics (results for diagrams etc.) as well as Quantum electrodynamics as defined on a grid.

But you know Zeidler died a few years ago, so we'll never have book 4 or more... Sad.
I have been doing mostly math in the last year's, for better or worse, except the quaternions and Bayesian stuff I need at work - but if you need to implement things, you usually can't dig too deep into alternatives. Also sad.

>>10946841
I write stuff into text files and eventually sort it into a wiki (e.g. the dokuwiki tool). It's always evolving but it sorta works for me

[Anonymous No.10946874]

>>10946841
I use notebooks with a cute alien on the cover.

[Anonymous No.10946895]

>>10946255
Is the separation between math and other fields completely artificial or is there some arbitrary contextual clues that inform people that what they are doing, for example, is "engineering" and not "math"?

[Anonymous No.10946913]

>>10946865
>I write stuff into text files
what sorta stuff do you write? i also do a wiki sorta thing but it's mostly a todo list with references

[Anonymous No.10946917]

>>10946874
just paper, all the time? what do you do with old notebooks?

[Anonymous No.10946922]

>>10946917
I store them in my bookshelf and occasionally destroy them.

[Anonymous No.10946930]

>>10946895
I'm not a mathematician, but I'd say that if you're proving or deriving something, that's maths. If you're calculating something, that's just computation. Here I'd define "calculating" as either sticking numbers into a formula, or using a rigid algorithm (simple analytical calculus that can easily be automated by a pocket calculator, or applying already-known numerical methods, would fall into this; tricky integration that require either human thought or an advanced solver, and proving/deriving a new numerical method, wouldn't).
Naturally while doing engineering you are very likely to need to compute things, and possibly even use "maths" according to the definition above.

Some would classify my "computation" as maths too, making it almost guaranteed that any engineering work will involve maths. Then the delineation is that plugging in a material's properties into a stress equation is maths, then concluding that you can or cannot use it to built a bridge - and repeating that for a variety of materials, and optimising for other things like cost, and designing proper safety margins - is engineering.

[Anonymous No.10946944]

>>10946930
>if you're proving or deriving something, that's maths
do lawyers do math when proving innocence or guilt? is deriving a new storyline for a book math? is logic math?

[Anonymous No.10946946]

>>10946913
Just md files with sections seperated by # or ## etc. and then bullet points or plain text.
https://gist.github.com/Nikolaj-K/951d44b393a92acc51f915fcb0e31cc2
When I feel like writing a plain text that I'll still understand in a few years, I translate it to e.g.
https://axiomsofchoice.org/ito_integral

>>10946895
People will disagree with this and then /sci/ gives each other shit about everything and in an unnecessary agressive way. So let me take some hits...

What's certainly true is that if you stand in a lab as a chemistry PhD 10 hours a day looking through a device and writing down how some liquits behave when mixed toghether - you're not doing math.
"Doing math" at an uni and for pure math will likely involve doing something that's trying to be innovative (and if not creatively, then at the very least in a way that notes down properties of things).
"Hard math" in engineering and applied physics might involve coming up with new tricks, but even solving complicated fluid dynamics numericalls will tend to involve the sort of conceptural setup that was establishe in math in the 1800'th. So Engineering work in differential equations will be barely interesting for mathematicans and mathematicans work on the same subject is of little help to the practical side.
Wwith high energy physics research (where physicists working in the field don't necessarily expect that there will be an experiment in their lifetime validating the ideas), you can say it's mostly a matter of interest in the field - while both do math. However, the half-life of math theories (hip trends) tends to be much longer than in physics departments. Let's say physics trends in academia can be years or a decade (say this and that path integral method in thi and that vaguely defined uncountably infinite dimensional vector space with applications for this and that sort of polymeres) while a lot of math theories survives for many decades (centuries in some cases, say combinatorics).

[Anonymous No.10946956]

>>10946946
>https://gist.github.com/Nikolaj-K/951d44b393a92acc51f915fcb0e31cc2
>https://axiomsofchoice.org/ito_integral
sounds similar enough to my workflow. I guess I just don't really know what to do with my repositories of solved problems and notes in notebooks from previous books and classes. Maybe burning them really is the right answer.

[Anonymous No.10946963]

>>10946946
>not using org

[Anonymous No.10946965]

>>10946944
Proving or deriving something based on the existing theorems of maths, I should have said.
Alternatively we could use a semantic argument to say that "proof" in math is not the same as "proof" in other areas, they just happen to use the same word: since in maths, proof is absolute (barring errors in the proof making it wrong), while in almost any other area it's impossible to prove something absolutely, especially given that we still don't have things like a perfect theory of the physical world or a disproof of some higher being (whether divinity, or operators of a simulation, or whatever). It's mostly a philosophical difference, but an important one: given a set of axioms, and a sound theory built from them, a sound proof built on that theory will be fundamentally correct based on those axioms, and no act of God or glitch in the matrix can change that.

[Anonymous No.10946971]

>>10946946
>https://www.youtube.com/watch?v=HrN7orXvu9k&feature=youtu.be
is this you anon?

[Anonymous No.10946975]

Please help me with this, it's driving me crazy.
Allowing for translations but not rotations, connected figures in 3d integer lattice space exist for each n of lattice points, allowing only connections of length one. Prove that the number of possible figures f(n) grows as a discrete function of n faster than any possible discrete polynomial, but slower than all discrete exponential functions.
For n=1 there is trivially only one solution.
For n=2 there are three ways, consisting of a connected pair of points differing from each other by a value of one in x, y and z respectively.
For n=3, f(n)=15. For n=4, f(n)=94.

[Anonymous No.10946984]

>>10946963
I've not actually used the wiki in a few years, that's an old snapshot. Pitch me org mode, I'm open.
As a matter of fact I need to write a good graphic tool replacing the graph on that page and then replace it. Right now I live with text files, mostly.

>>10946971
Yeah, I've posted this in the previous thread too I think.

Btw., and especially for the one (or few) guy who is aggressively constructive vist and lurking here too, today I came across this book upload on archive

https://arxiv.org/abs/1906.01803
>Constructive probability

Seems to be by a guy who worked on Bishops approach in the 80s (and then went into the finance sector).
Really like it a retired guy would come back to do this.

[Anonymous No.10947008]

>>10946975
Let g(n) count the same thing without translations.
Clearly g(n) <= 6^n since there are 6 directions, and g(n) >= 3^n if you consider going only in 3 directions (only taking increasing steps in each coordinate).
Now note that any n-length path is contained in nxnxn box, and hence has at most (n+1)^3 translations.
So f(n) >= 3^n/(n+1)^3 which makes it exponential.

[Anonymous No.10947009]

>>10946255
There’s an arab mathematician? I thought they went extinct after the golden age of islam.

[Anonymous No.10947013]

>>10946975
Show that it grows faster than any x^n through the usual trickery, a.k.a. translation of variables.

[Anonymous No.10947019]

>>10946984
>Pitch me org mode
well supposing you took notes in org you could then generate a page for your wiki out of it (there's many different export options).
the syntax is similar but it comes with the "burden" of learning emacs.
I'm calling it a burden since it rquires a a chunk of time spent on setting it up and learning the basics - only then you get to learn org.
and why would you want to learn org?
well apart from the great exporting capabilities you are getting your hands on a tool than can do everything from taking notes, scheduling your day and calculating your spending (yes it has a purely text-based spreadsheet capabilities)
overall a very pleasant tool to work with - especially if you have even the slightest of sparks of autism (which I assume you do, given the circumstance)

[Anonymous No.10947040]

>>10947009
If he's Banach, then he should be Polish.

>>10946975
I'm confident that >>10947008 has figured the main argument out. Does the job not just amount to going from n-1 to n and figuring out all the ways in which the new structure can be different?
>>10947008
Not that that changes the big O behaviour, but can't you not also append on the tail of th thing? And can you even go back? So I'd say not *6 each step but *10.

Btw. this sounds like this in 3D

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

>>10947019
I "used" Emacs before, actually, which is to say I spend a few hours in the manual and ran some commands and looked at some text files (for FORTRAN code in computational chemistry from god knows which decade). I'm afraid it's not gonna happen, to be honest, but thanks for the pitch. Also, I'm not even as autistic as one could assume.

>>10946984
Btw. after reading pic related today I found that the LPO and LLPO that I had posted in the >why axioms thread also has a Wikipedia page

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

Reading on in that book btw. I also ended up discussing with a few type theorists:
>do you like the principle of explosion?
I personally a really not a fan - what's your guys take? I mean I don't like it even if you adopt LEM.

[Anonymous No.10947058]

>>10947040
Looking a bit deeper into the Polyomino, I think it might be that as a research topic one may find into under the name "polycube", see e.g. the references therein,
https://en.wikipedia.org/wiki/Polycube
e.g.
https://arxiv.org/pdf/1311.4836v1.pdf

[Anonymous No.10947088]

>>10946984
>Pitch me org mode
in addition to what others have said, it does a LOT while being a minimalist plain text 'mode'. No clutter of hopping through menus etc or having a strong interface structure forced on you. So while it has spreadsheet/graphing/etc capabilities, you wouldn't notice at first, you'd think you were just screwing around with a plain text document until you ran some org functions. It doesn't force you to use it for an agenda or anything like that. you can use it as much or as little as you like with minimal pain points. Personally I use the shit out of it and most my interaction with my computer is either my browser or emacs, and 90% of my time in emacs is org mode.

It is pleasant to turn notes into tasks, references, etc and have these all searchable and dynamically displayed via metadata like date, tags, priorities, etc. Very flexible and mature tool. also, working w/ latex is slick. In essence, rather than using your md file with ## you could instead use org-mode with **, but you get a lot more power if you want it. I see now you already declined the other pitch though so /shrug

just out of curiousity what's your day to day like anon? are you doing postgrad research?

[Anonymous No.10947094]

>>10947058
The problem seems to just involve enumerating the distinct 90 degree rotations of the polycubes

[Anonymous No.10947387]

Looking for a rigorous and readable statistics book. Any suggestions /mg/?

[Anonymous No.10947496]

bros I miss the putnam threads

[Anonymous No.10947531]

>>10947040
>>10947019
org-mode is pretty usable with evil-mode too. Can download something like doom emacs if you really can't be bothered trying to customise it yourself, but want something more streamline and well-integrated than the default.
This way you barely have to learn emacs if at all, and can start using org-mode right away.

[Anonymous No.10947609]

https://arxiv.org/pdf/1909.02205.pdf
>The answer to a conjecture on the twin prime
>Mbakiso Fix Mothebe, Dang Vo Phuc
>(Submitted on 5 Sep 2019)

>Let p_1=2,p_2=3,p_3=5,…,p_n,… be the ordered sequence of consecutive prime numbers in ascending order. For a positive integer m, denote by π(m) the number of prime numbers less than or equal to m. Let [] denote the floor or greatest integer function. In this paper, we show that for all n≥1:
>[math] \left[\frac{p^2_{n+1}}{n+1} \right]
\leq \pi\left(p^2_{n+1} \right). [/math]
>As a consequence, we see that there are infinitely many primes (Euclid's theorem). Then, we prove that if we let π_2(m), denote the number of twin primes not exceeding m, then for all n≥2:
>[math]\left[\frac{p^2_{n+3}}{3(n+2)} \right] \leq \pi_2\left(p^2_{n+3}
\right)[/math]
>and thereby prove the twin prime conjecture, namely that there are infinitely many prime numbers p for which p+2 is also a prime.

[Anonymous No.10947611]

>>10947609
>Let p_1=2,p_2=3,p_3=5,…,p_n,… be the ordered sequence of consecutive prime numbers in ascending order. For a positive integer m, denote by π(m) the number of prime numbers less than or equal to m. Let [] denote the floor or greatest integer function. In this paper, we show that for all n≥1:
>[math] \left[\frac{p^2_{n+1}}{n+1} \right] \leq \pi\left(p^2_{n+1} \right). [/math]
>As a consequence, we see that there are infinitely many primes (Euclid's theorem). Then, we prove that if we let π_2(m), denote the number of twin primes not exceeding m, then for all n≥2:
>[math]\left[\frac{p^2_{n+3}}{3(n+2)} \right] \leq \pi_2\left(p^2_{n+3} \right)[/math]
>and thereby prove the twin prime conjecture, namely that there are infinitely many prime numbers p for which p+2 is also a prime.

[Anonymous No.10947612]

I am having hard time understanding number theory theorems. Like how do you digest fundamental thoerem of arithmetic.

[Anonymous No.10947618]

>>10947612
I never considered how anybody could have an intuition that speaks against it.

[Anonymous No.10947621]

>>10947612
accept it and don't question anything

[Anonymous No.10947624]

>>10947387
the wiki has about a half dozen recommended texts why not try that before asking for help?

[Anonymous No.10947635]

a-ano sumimasen! shitsumonga arun desukedo...

/sci/, you're the smartest board. I need your help onegaishimasu. How do I do this problem?

[Anonymous No.10947648]

>>10947635
plug it into wolframalpha.com

[Anonymous No.10947661]

>>10947648
I might be a brainlet because it doesn't seem to give me the answer I need.

[Anonymous No.10947677]

>>10947635

[Anonymous No.10947683]

>>10947635
Scuff your knees and ask the professor nicely.

[Anonymous No.10947701]

>>10947635
4 years of math at uni and I even forget how to do this.

[Anonymous No.10947705]

>>10947683
He's a graduate student in his last year. He scares me because he will most definitely bully me. I need to study more.

[Anonymous No.10947734]

>>10947705
>I'd sooner be bullied by useless autists on a swedish crop rotating forum than by someone who can actually be helpful in real life
Reconsider.

[Anonymous No.10947744]

>>10947705
I'm sorry, but the union would get mad at me for stealing a bullying opportunity from a fellow professor.

[Anonymous No.10947827]

>>10947624
nothing on stats as far as I can tell

[StupidProofs No.10948087]

If p is prime then prove or disprove that p+2 is prime.

[Anonymous No.10948112]

>>10946831
>String and Quantum Field theories.
Aren't you forgetting something? (PLEASE mention TQFT)

[Anonymous No.10948178]

>Khan Academy
Oh Here is Fermat's Little theorem. We will show with beeds and shit how this is so beautiful visually. Proofs? Who cares about proofs. hahaha. fuck these mainstream mathlets who tries to be aware of maths by using examples to show that they know maths.
Those who watch Khan Academy are literal 130IQ.

[Anonymous No.10948195]

https://arxiv.org/pdf/1909.01898.pdf
>On the generic part of the cohomology of non-compact unitary Shimura varieties
>Ana Caraiani, Peter Scholze
>(Submitted on 4 Sep 2019)

>We prove that the generic part of the mod l cohomology of Shimura varieties associated to quasi-split unitary groups of even dimension is concentrated above the middle degree, extending previous work to a non-compact case. The result applies even to Eisenstein cohomology classes coming from the locally symmetric space of the general linear group, and has been used in [ACC+18] to get good control on these classes and deduce potential automorphy theorems without any self-duality hypothesis.
>Our main geometric result is a computation of the fibers of the Hodge--Tate period map on compactified Shimura varieties, in terms of similarly compactified Igusa varieties.

[Anonymous No.10948197]

I'm starting to like maths again. I hope you have nice weekends, too!

[Anonymous No.10948204]

https://arxiv.org/pdf/1909.01434.pdf
>Towards Hilbert's Tenth Problem for rings of integers through Iwasawa theory and Heegner points
>Natalia Garcia-Fritz, Hector Pasten
>(Submitted on 3 Sep 2019)

>For a positive proportion of primes [math]p[/math] and [math]q[/math], we prove that [math]\mathbb{Z}[/math] is Diophantine in the ring of integers of [math]\mathbb{Q}(\sqrt[3]{p},\sqrt{-q})[/math]. This provides a new and explicit infinite family of number fields [math]K[/math] such that Hilbert's tenth problem for [math]O_K[/math] is unsolvable. Our methods use Iwasawa theory and congruences of Heegner points in order to obtain suitable rank stability properties for elliptic curves.

[Anonymous No.10948212]

>>10947609
>>10947611
Lads...

[Anonymous No.10948215]

>>10947827
you’re not going to make it

[Anonymous No.10948216]

>>10947496
start 'em up boi

[Anonymous No.10948224]

>>10947635
for the domain: input of a log has to be >0, so set 6t+64 >0 and solve for t
should be t> -64/6 or t>-32/3

for range: logs range is all real numbers, (-infinity, infinity)

for vertical intercept: set t=0, solve for y.
should be (0,-1)

for horizontal: set y=0 and solve for t through exponentiation of 4 to get rid of the log. move -4 to the other side of the equation first though.
should get (32,0)

for vertical asymptote this is the value t cannot be, so set 6t+64 = 0 and solve for t.
t=-64/6=-32/3

[Anonymous No.10948256]

>>10947612
hello, i'm a digestive aid here to try and help:

a number can be represented by a factorization tree.

a factorization tree starts at number and splits into divisors - unless it's prime, in which it doesn't really cuz it's factorization is just prime*1. now pack up ur bags kid cuz we're moving on to the next paragraph.

the fundemental theorem of arithemtic just states that some numbers are prime and have irreducible factorization trees, while others are made of primes (in other words, they reduce down to primes / their factorization tree is made of primes).

either a factorization tree is 0 nodes deep or it's more. those that are 0 nodes deep we call prime. those that are not will eventually meet a dead end: this dead end is a prime because it is 0 nodes deep.

if it were not true then I think it's fair to say numbers could have infinite factors (e.g no dead end, they could not be factored into irreducible forms / primes). but hey i'm a noob and just skimmed the def'n on wikipedia

[Anonymous No.10948262]

>>10948256
please go back or at least lurk for another 2-3 months before posting again fag

[Anonymous No.10948268]

>>10948262
>fag
Why the homophobia?

[Anonymous No.10948270]

>>10948262
>>10948268
Yeah fag, why so homophobic?

[Anonymous No.10948278]

>>10948262
u mad? post a real critique next time ya homophobic NOOB

[Anonymous No.10948281]

>>10948268
How is "fag" related to anything homosexual? Are you interpreting cigarettes as phallic objects to be put in your mouth or something?

[Anonymous No.10948350]

>>10948281
>How is "fag" related to anything homosexual?
https://en.wikipedia.org/wiki/Category:Homophobic_slurs

[Anonymous No.10948360]

>>10948350
I see. It is only natural that a low-brow person would project their coprolalia onto everything.

[Anonymous No.10948367]

>>10948268
[the homosexuals] not only fail from resisting the weakness [of fallen human nature] .... but they do even worse when they commit the cursed sin against nature. Like the blind and stupid, having dimmed the light of their understanding, they do not recognize the disease and misery in which they find themselves. For this not only causes Me nausea, but is disgusting even to the devils themselves whom these depraved creatures have chosen as their lords.

For Me this sin against nature is so abominable that for it alone five cities were destroyed by virtue of the judgment of My Divine Justice, which could no longer bear their iniquity ....

It is disgusting to the devils not because evil displeases them or because they find pleasure in good, but rather because their nature is angelic and flees upon seeing such a repulsive sin being committed. For while certainly it is the devil that first strikes the sinner with the poisoned arrow of concupiscence, nonetheless when a man actually carries out such a sinful act, the devil goes away.

-- Dialogues of St Catherine of Siena

[Anonymous No.10948388]

>>10948367
ok retard

[Anonymous No.10948391]

>>10946963
Hey fellow emacser

[Anonymous No.10948460]

>>10948367
I don't see the relevance to this board. Perhaps you meant to post this on /lit/ or /his/?
>>10948388
Why the ableism?

[Anonymous No.10948644]

>>10948087
>prove that all even numbers are prime

[Hirnlein No.10948706]

What do you guys think of Knuth and The Art of Computer Programming?

Have you tried to read it? I've heard it's quite gruelling

[Anonymous No.10948727]

>>10948706
only read SICP

[Hirnlein No.10948733]

>>10948727
Is that "read" in the past indicative, or "read" as an imperative?

[Anonymous No.10948746]

>>10948706
sounds like neither science nor mathematics, perhaps >>>/g/ is better suited to your needs and interests anon? please try to keep your posts on topic this general is for mathematics students and mathematicians. thank you

[Hirnlein No.10948751]

>>10948746
Is this the anti-CS meme I hear about on /sci/?
TAOCP *is* mathematics.

[Anonymous No.10948814]

suppose |a − b| ≤ |a − c| + |c − b| . and a = -5 and b =1

find c1 so that |a − b| = |a − c1| + |c1 − b| .

Am I retarded or is the answer 0?
You get 6 = 5+c1 + c1+1
6-6 = c1

I'd answer it (correctly) myself, but it's literally not in my calculus book and I've never heard Triangle inequality before today

[Anonymous No.10948860]

>>10948814
[math]
|a − b| = |a − c1| + |c1 − b|
[/math]
plugging in a = -5 and b = 1
[math]
|(-5) − 1| = |(-5) − c1| + |c1 − 1|
[/math]
reducing to
[math]
6 = |5 + c1| + |c1 − 1|
[/math]
we have 3 ranges to consider
[math]
(-\infty; -5), [-5; 1), [1, \infty)
[/math]
proceed from here

[Anonymous No.10948878]

>>10948644
odd numbers too

[Anonymous No.10948884]

>>10948860
>proceed from here

[Anonymous No.10948902]

[math] \left( \frac{1+|x|^2}{1+|y|^2} \right)^t \le 2^{|t|} (1+|x-y|^2)^{|t|} [/math]

[Anonymous No.10948907]

>>10946255
Looks like Jude Law.

[Anonymous No.10948939]

>>10948860
the answer is [−5;1), but I can't tell you mathematically why that is, but it's just common sense since -∞ and ∞ makes no sense

[Anonymous No.10948959]

>>10948939
very well, I shall demonstrate what needs to be done
[math]
in (-\infty; -5) the equation becomes
6 = (-(5+c1)) + (-(c1-1))
-5 = c1
-5 \notin (-\infty; -5)
[/math]
>therefore no solutions in this range
[math]
in [-5; 1) the equation becomes
6 = (5+c1) + (-(c1-1))
6 = 6
[/math]
>therefore all numbers in the range are valid solutions
[math]
in [1; \infty) the equation becomes
6 = (5+c1) + (c1-1)
1 = c1
1 \in [1; \infty)
[/math]
>therefore 1 is also a valid solution

summing it up, the solution becomes
[eqn]
c1 \in [-5; 1]
[/eqn]

[Anonymous No.10948962]

>>10948959
god i love latex

[Anonymous No.10949132]

>find a line that is parallell to 5x+3y=-4 and passes through the point (5,1)

all I did was remember back to vectors and how we found parallelle lines and did 5*5 and 3*1 which is 28

so the line is 5x+3y = 28

but I feel like this isn't a sufficient answer or even the correct way of doing it because we have no vectors in this course but I can't remember how to solve it any other way

[Anonymous No.10949157]

>>10949132
this is not sqt

[Anonymous No.10949176]

>>10949132
[eqn]
\mathcal{BRAINLET}
[/eqn]

[Anonymous No.10949178]

>>10949157
>>10949176

[Anonymous No.10949360]

>>10948112
give me a quick rundown on TQFT please
Are there any good survey articles, or textbooks? I'm having trouble getting a picture of that field. Also, what's your stance on perturbative AQFT?

[Anonymous No.10949428]

>>10949360
TQFT is a symmetric monoidal covariant functor [math]Z:\left(\operatorname{Bord}_{n,n-1}^G,\coprod\right) \rightarrow \left({\bf Vect}_\mathbb{C},\otimes\right)[/math] of the bordism category (with [math]G[/math]-structure) into the category of [math]\mathbb{C}[/math]-linear vector spaces. More generally you can use any symmetric monoidal category as a target, but with [math]{\bf Vect}[/math] you're essentially finding linear representations of the bordism category, which is encodes tremendous amount of topological data (though the cobordism hypothesis reduces the dependence on this data of [math]Z[/math] to a single point).
What this entails is that [math]Z(M) \in \mathbb{C}[/math] gets you very powerful topological invariants for compact closed bordisms [math]M[/math], called the partition function, which can distinguish more [math]n[/math]-folds than popular cohomology theories (typically in low dimensions).
On the other hand, the Levin-Wen construction relates the 2D modular functor [math]Z_c[/math] (obtained from the TQFT [math]Z[/math] on [math]\operatorname{Bord}_{2,1}[/math] equipped with braiding and ribbon relations) to 1D local projector Hamiltonians [math]H[/math], in the sense that [math]Z_c(M) = \operatorname{tr}_\mathcal{F}e^{-\beta H}[/math] for some colouring [math]\mathcal{F}[/math] of a triangulation of [math]M[/math]. What this means is that essentially all 1D conformal phenomena, such as quasiparticle fusion relations and the anomalous dimension, can be captured by (1+1)D TQFTs. This correspondence is conjectured to work for all [math]n \geq 1[/math], and major work has been done to prove this on spheres [math]M = S^n[/math] via the [math]C[/math]-theorem.
>what's your stance on perturbative AQFT?
It's cool.

[Anonymous No.10949453]

is f(x)=0 differentiable

[Anonymous No.10949526]

>>10949453
>>10949453
well yes in riemann-lebesgue sense but actually no

[d No.10949546]

Just surveyed Wikipedia articles that discuss variants of a bunch of the derivative.
Is someone missing their favorite instance?

The categorization is a bit rough - plx let me know if someone feels it's somewhere _entirely_ off

########################

https://en.wikipedia.org/wiki/Derivative
https://en.wikipedia.org/wiki/Generalizations_of_the_derivative

#### [Calculation rules]
https://en.wikipedia.org/wiki/Differentiation_rules
https://en.wikipedia.org/wiki/Del_in_cylindrical_and_spherical_coordinates
https://en.wikipedia.org/wiki/Vector_calculus_identities
https://en.wikipedia.org/wiki/Vector_fields_in_cylindrical_and_spherical_coordinates
https://en.wikipedia.org/wiki/List_of_derivatives_and_integrals_in_alternative_calculi


## Differential operator calculus perspective
As "higher-order" function and function comprised of derivatives:
https://en.wikipedia.org/wiki/Differential_operator

### D^1
https://en.wikipedia.org/wiki/Theta_operator

### D^1, multivariate
https://en.wikipedia.org/wiki/Partial_derivative
https://en.wikipedia.org/wiki/Directional_derivative
https://en.wikipedia.org/wiki/Total_derivative

https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant
https://en.wikipedia.org/wiki/Gradient
https://en.wikipedia.org/wiki/Divergence
https://en.wikipedia.org/wiki/Curl_(mathematics)

https://en.wikipedia.org/wiki/Directional_derivative
https://en.wikipedia.org/wiki/Vector_field
https://en.wikipedia.org/wiki/Lie_derivative
https://en.wikipedia.org/wiki/Conformal_Killing_vector_field

### D^2, multivariate
https://en.wikipedia.org/wiki/Hessian_matrix
https://en.wikipedia.org/wiki/Elliptic_operator
https://en.wikipedia.org/wiki/Laplace_operator
https://en.wikipedia.org/wiki/Semi-elliptic_operator

[∂ No.10949549]

## D^n
Non-linear operators using derivatives with a simple chaining rule calculus
https://en.wikipedia.org/wiki/Schwarzian_derivative

Considering differential operators on a special class of functions, and then
extending the space of those operators in "natural" ways. E.g. Letting
the dual/Fourier-space representation of the operators depend on variables:
https://en.wikipedia.org/wiki/Pseudo-differential_operator

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


## Differential geometry
https://en.wikipedia.org/wiki/Exterior_derivative

#### Complex
https://en.wikipedia.org/wiki/Complex_differential_form
https://en.wikipedia.org/wiki/Wirtinger_derivatives

#### context with connection
https://en.wikipedia.org/wiki/Exterior_covariant_derivative
https://en.wikipedia.org/wiki/Covariant_derivative


## Other limit definitions
### Weaker
https://en.wikipedia.org/wiki/Strict_differentiability
https://en.wikipedia.org/wiki/Dini_derivative
https://en.wikipedia.org/wiki/Semi-differentiability
https://en.wikipedia.org/wiki/Subderivative

### Topological
https://en.wikipedia.org/wiki/Gateaux_derivative
https://en.wikipedia.org/wiki/Differentiation_in_Fr%C3%A9chet_spaces

#### Banach
https://en.wikipedia.org/wiki/Fr%C3%A9chet_derivative
https://en.wikipedia.org/wiki/Quasi-derivative

##### Uncountably infinite dimensional
https://en.wikipedia.org/wiki/Functional_derivative


## Numerics and finite differences
https://en.wikipedia.org/wiki/Numerical_differentiation
https://en.wikipedia.org/wiki/Difference_algebra
https://en.wikipedia.org/wiki/Difference_quotient
https://en.wikipedia.org/wiki/Finite_difference
https://en.wikipedia.org/wiki/Umbral_calculus
https://en.wikipedia.org/wiki/Finite_difference_coefficient
https://en.wikipedia.org/wiki/Template:Numerical_PDE
https://en.wikipedia.org/wiki/Recurrence_relation#Relationship_to_difference_equations_narrowly_defined
https://en.wikipedia.org/wiki/Fermat_quotient

[give her the D No.10949553]

## Algebraic approaches
(this needs to be more sorted)

Axioms and general
https://en.wikipedia.org/wiki/Derivation_(differential_algebra)
https://en.wikipedia.org/wiki/Formal_derivative

Lots of results, e.g. in the multivariable treatment, can be and is often presented very algebraically. E.g. all the Lie-derivative stuff.


## Abstract algebra
https://en.wikipedia.org/wiki/Weyl_algebra
https://en.wikipedia.org/wiki/Hasse_derivative
https://en.wikipedia.org/wiki/Differential_algebra
https://en.wikipedia.org/wiki/Differential_calculus_over_commutative_algebras

### Tied to number theory
https://en.wikipedia.org/wiki/Arithmetic_derivative
https://en.wikipedia.org/wiki/P-derivation

### Tied to topology
https://en.wikipedia.org/wiki/Differential_calculus_over_commutative_algebras
https://en.wikipedia.org/wiki/Jet_(mathematics)
https://en.wikipedia.org/wiki/Jet_bundle

#### Special topics
https://en.wikipedia.org/wiki/Hasse%E2%80%93Schmidt_derivation
https://en.wikipedia.org/wiki/Pincherle_derivative
https://en.wikipedia.org/wiki/D-module
https://en.wikipedia.org/wiki/Differential_graded_algebra
https://en.wikipedia.org/wiki/Differentially_closed_field
https://en.wikipedia.org/wiki/K%C3%A4hler_differential
https://en.wikipedia.org/wiki/Q-derivative


## Integral related variants
https://en.wikipedia.org/wiki/Weak_derivative
https://en.wikipedia.org/wiki/It%C3%B4%27s_lemma
https://en.wikipedia.org/wiki/Differintegral
https://en.wikipedia.org/wiki/Radon–Nikodym_theorem

#### Fractal / Fractional
https://en.wikipedia.org/wiki/Fractal_derivative
https://en.wikipedia.org/wiki/Fractional_calculus
https://en.wikipedia.org/wiki/Gr%C3%BCnwald%E2%80%93Letnikov_derivative

[Anonymous No.10949570]

so how does [math]\mathcal{L}\{\sin(t-\tau)\}[/math] work?
or do you ignore [math]\tau[/math] and use [math]g(t) = \sin(t)[/math] ?

this book seems kind of shitty so far

[Anonymous No.10949576]

>>10949428
Thanks! So when working in 1+1 dim. TQFTs instead of the framework of CFT, am I right to assume that this basically gives "easier" ways to compute things? Or allows better computer implementation?

[Anonymous No.10949579]

>>10949570
What exactly is the problem?

[Anonymous No.10949596]

>>10949579
I am not sure if the application of the convolution theorem to [math](f * g)(t)[/math] uses the shifted version of g (by tau) or if it uses the original g(t), or if this even makes a difference.
The book is very not clear on this.

[Anonymous No.10949645]

>>10949576
I think "easier" depends on what you want to get at the end. Given the fusion relations as well as an affine representation thereof, you can compute, with TQFT, [math]Z_c(\Sigma_{z_1,\dots,z_m})[/math] on punctured Riemann surfaces, where irreducible characters for the affine reps are inserted at the puncture [math]z \in \Sigma[/math]. This is equivalent to the correlations [math]\langle \phi(z_1),\dots,\phi(z_m)\rangle[/math] on the CFT side, and completely bypasses dealing with highest-weight irreps of the Virasoro primaries. The same goes for the quantum spins (braiding statistics), which you can obtain from Vafa's theorem.

On the other hand, if you want the central charge [math]c[/math] or the anomalous dimension [math]\eta[/math], you need to compute the singular part of the stress-energy tensor [math]\langle T(z)T(w)\rangle \sim \frac{c}{(z-w)^{4-\eta}}[/math]. This is evidently easier with CFT since [math]T[/math] is a bidifferential you can perform contour integrals over, while for TQFT you'll need to assign Hodge line bundles over the moduli space of Riemann surfaces (for which [math]Z[/math] maps into the fibre spaces of these line bundles) and then analytically continue [math]Z[/math] to the compactified moduli, then use factorization to extract the singular part via [math]T \sim \partial Z[/math]. At this point you might as well just be doing CFT.

[Anonymous No.10949652]

>>10949645
Oops I meant [math]T\sim \partial \ln Z[/math].

[Anonymous No.10949701]

>>10949546
>>10949549
>>10949553
You might want to post something more original, all you're doing here is linking the work of others, it's pretty derivative.

[Anonymous No.10949720]

>>10949701

[Anonymous No.10949774]

>>10949132
find the slope of 5x+3y=-4, m=-5/3
use point slope to find the equation.
(y-1)= -5/3(x-5)

[Anonymous No.10949815]

>>10949428
do you have a good starting text for mathematician ?

[Anonymous No.10949826]

>>10949815
https://arxiv.org/abs/1210.5100

[Anonymous No.10949848]

>>10946255
Is it necessary to get a Ph.D in math to do big boy maths or can you just do it on your own?

[Anonymous No.10949864]

>>10949848
What do you mean by "do"?
I don't think you'll find many (any?) people in the last 10 years that did relevant stuff without having an academic title.
Shanon is the extreme counterexample who invented a math field as his bachelor thesis, but generally it won't happen.

>>10949826
What are some more recent results (classifications) in the field?

[Anonymous No.10949872]

>>10949848
What do you mean by "do"?
I don't think you'll find many (any?) people in the last 10 years that did relevant stuff without having an academic title.
Shannon is the extreme counterexample who invented a math field as his undergrad thesis (iirc), but generally it won't happen.

>>10949826
What are some more recent results (classifications) in the field?

[Anonymous No.10949880]

>>10949848
you can write papers and if they're good you can get published. nobody will hire you though.

[Anonymous No.10949905]

>>10948215
post your grades

[Anonymous No.10949908]

>>10949872
Gauging global finite [math]G[/math] symmetries in fermionic TQFT.
https://arxiv.org/abs/1812.11959
3D TQFTs with boundary/defect data.
https://arxiv.org/abs/1710.10214
Complete classification of extended invertible TQFTs.
https://arxiv.org/abs/1712.08029
Complete symmetry classification of topological orders.
https://arxiv.org/abs/1604.06527
Classification of (3+1)D liquid topological orders.
https://arxiv.org/abs/1704.04221
https://arxiv.org/abs/1801.08530
Twisted TQFT from crystallographic T-duality in CFT.
https://arxiv.org/abs/1806.11385

[Anonymous No.10950078]

>>10949826
Thanks again m8!

[Anonymous No.10950121]

>>10949872
no academic title != not getting a Ph.D

[Anonymous No.10950122]

>>10949905
absolutely pathetic retard

[Anonymous No.10950164]

>>10949553
gay

[Anonymous No.10950539]

>>10949596
The "... minus tau" is part of the definition of convolution. The integral is w.r.t. tau; t is a free variable within the integral.

Also: the equation on the line below the integral would be more accurately written as
y(t) - (y * sin)(t) = t.

[Anonymous No.10950656]

>teacher: find the area of a circle with radius R using integration
>me
[math]Area = \int_0^1\pi R^2 \,dt[/math]

[Anonymous No.10950709]

WHATS BEST INFORMATION THEORY TEXBOOK

[Anonymous No.10950728]

>>10950709
https://en.wikipedia.org/wiki/Information_theory

[Anonymous No.10950822]

>>10949908
Thx. Can't quite read it, but I'm not sure if I expected I would.
A lot of asians in the field, huh. I like how they all add colorful graphics.

Is it called Z because the functor sort of directly relates to the partition function, or does the partition functor live independently on either of the categories (domain/codomain of the functor)? I mean I don't see how e.g. the formal parameter (say beta) comes in.

[Anonymous No.10950965]

Is transsexuality and bisexuality common in mathematicians?

I see lots of androgynous pics thrown about in this gen and the women in math I see tend to be fairly masculine looking

[Anonymous No.10950969]

What are some less known mathematics subjects, guys?
I want to see some different stuffs beyond what my uni already covers.

[Anonymous No.10951120]

>>10950969
if less known means rare, i.e. relatively few groups:
crystallography
topological group theory
information geometry
incidence geometry
numerical algebra (in particular Groebner stuff)
operator algebras
computational proof theory (e.g. HoTT + /g/)
logic (yes it's rare nowadays)
non-standard analysis
partial differential relations (what a shame)
h-principle (related to above, probably because it's difficult as fuck)
"analytical" algebraic geometry, also because hard imo (I'm trying to do that, check papers by Deligne if interested)
tropical geometry
origami math
variational bi-complex stuff (physicists don't like higher derivatives than of order 2, hence only a babby version of Noethers theorem in most phys lit, mathematicians rarely enjoy calculating)

I hope that someone proves me wrong on at least one of the topics listed above.

[Anonymous No.10951270]

>>10950822
Mathematically speaking [math]\beta[/math] controls the length of the "+1"-th dimension. It's inessential to the topology (as long as it's not 0).

[Anonymous No.10951272]

>>10951120
Check the msri summer topics, tropical geometry is becoming a bigger industry. Some folks like Camillo De Lellis have connected the work of gromov to the study of turbulence, so I feel like PDR and the h-principle (which in itself is used a lot, don't know why you listed that as less known) should be getting broader exposure in the pde community. Tao like nonstandard analysis, so there's that. People also care about topological groups, at least when there's a nice representation.

[Anonymous No.10951358]

>>10950965
mathematical ability is strongly associated with male brain structure and autism (hyper-masculinized brain) so no.

[Anonymous No.10951395]

>>10950965
4chan is full of social undesirables and those who frequent /mg/ (re: math phds) have been here longer than average.

[Anonymous No.10951411]

Quick question, is there a typo here? Shouldn’t it be F’(A)->F(A) ?

[Anonymous No.10951442]

What should I name my large-scale NLP interior point solver, /mg/?

[Anonymous No.10951476]

sup bros
>assuming i dont hard code my primality test, can it be shown that if my primality test is correct for all integer k < N, then it must be valid for all integer m >= N?

[Anonymous No.10951555]

>>10951411
Yes.

[Anonymous No.10951591]

>>10951395
you just want to suppress true progress of society

[Anonymous No.10951600]

>>10951591
>no TIMESAND____ image filename
>posting that book and not being Tooker
..the fug?

[Anonymous No.10951659]

>posting book
>not buying it
>me on left

[Anonymous No.10951702]

>>10950969
Incidence geometry was spot on, it is one of those subjects that used to be very popular and faded into oblivion. It could be said to be regaining some traction with the theory of buildings that is currently finding more and more applications.
Other relatively arcane subjects (depending on where you study of course, but pretty uncommon where I live) include:
semigroup theory
set theory
higher categories
homotopy theory
"pure algebra", as in eg. algebraic theory of quadratic forms, algebras with involutions, cohomological invariants etc.
Arakelov geometry

[Anonymous No.10951704]

>>10951120
If rare means "outside the mathematical main stream" then tropical geometry and analytical AG don't really belong here. Tropical geometry has been a major part of AG since Mikhalkin's work connecting it to mirror symmetry, and I don't know anything Deligne has done that could be described as being outside the mainstream.

Large swaths of what you might call "topological group theory" like p-adic / adelic groups are quite mainstream too.

A problem common to some (not all) of your topics is that they don't readily separate interesting from less interesting objects -- good definitions often exclude pathological objects. Some things (information geometry for example) I expect to see in statistics rather than mathematics; other things straddle some other subject besides mathematics.

I don't think crystallography is a real subject in math as it is practiced today (what hasn't been classified?). Reflection groups / Coxeter systems are of course, but those are a mainstream subfield of representation theory.

[Anonymous No.10951724]

>>10951659
hey Tooker, just curious, do you see the face coming out of the mask when it's turned around, or does the illusion not trick your eyes?

[Anonymous No.10951747]

>>10951120
>partial differential relations (what a shame)
I feel this isn't really rare at all.

The information theory is debatable. At least all the quantum computer people need to take a course in some information theory - but maybe that's more in physics and CS and you're thinking about a math degree. Similar with crystallography in physics and logic in CS.

>>10951442
ballsdeep

[Anonymous No.10952203]

>>10951555
Thanks

[Anonymous No.10952500]

Is it true that most Math PhD students would get 100% on the IMO?

[Anonymous No.10952562]

when does complex numbers stop being spooky and/or cumbersome

[Anonymous No.10952669]

>>10946723
At looked at that book (series) today at the library. Seems like he really loved to write very thick books in general. Actually makes me think he didn't bother much about sorting out and rewriting things, but I might well be wrong.

>>10952500
smells like something along the lines fitting of
f2(n) := n - f1(n) + g(n)
and turing f1 such that when g maps to the same thing, f1 doesn't. Just a blue guess

>>10952562
from the start

[Anonymous No.10952715]

>>10952500
>Is it true that most Math PhD students would get 100% on the IMO?
no

[Anonymous No.10952741]

>>10952500
No because math PhDs usually work by understanding the subject thoroughly and expanding upon it, instead of wasting their time with meme problems by grinding useless techniques.

[Anonymous No.10952772]

>>10952741
let me guess, you can't do neither competition problems nor higher math?

[Anonymous No.10952773]

What is the best way to relearn math from the start? What are the best textbooks? I would also like to understand the unconventional aspects of calculation such as in this video https://www.youtube.com/watch?v=hesKQ_y1P7k&t=7s.. If it's a meme just tell me but I want to understand mathematics to its very core.

[Anonymous No.10952794]

>>10952772
I think he's right, nobody would get 100% at IMO unless they explicitly trained for it, not even the good math Profs. Those problems are really mostly very unnatural applications of theorems or combinatorical principles. Unnatural in that it's mostly dubios in which context those problems would have arisen.

[Anonymous No.10952801]

>>10952773
most calculation tricks are a total waste of time
it is more important to have an innate understanding of the very basics
on a basic level it is say stuff like
>thinking about numbers as a number line
>how does operations like addition or subtraction move up/down this line
>probability, combinatorics, branching trees
>ratios/percentages
>what are actually functions or equations
just stuff like this, instead of memorizing formulas or tricks

t. no education in pedagogy so I might just be talking shit though

[Anonymous No.10952878]

What's the most interesting millennium problem in your opinion? I have to write a paper on one of them, but am not drawn to any in particular.

[Anonymous No.10952894]

>>10952878
historically riemann
most easy to find stuff about NP

[Anonymous No.10952897]

>>10952878
Let's by real here, you'll not end up writing about Hodge or Birch and Swinnerton-Dyer.
Navier Stokes at least has an approachable context and there's lots of info out there on the Riemann hypothesis.
P vs. NP is the most interesting to me.
I expect you'll take about either of the last two.

[Anonymous No.10952934]

What is game theory good for?

[Anonymous No.10952938]

>>10952934
designing games

[Anonymous No.10952943]

>>10952934
writing papers about game theory

[Anonymous No.10952949]

>>10952801
tell it to the finance firm interviewer asking you to calculate 89^3 in 2 seconds

[Anonymous No.10952954]

>>10952934
designing books on games

[Anonymous No.10952965]

>>10952949
>finance firm
sorry, I thought we were talking about humans not robot drones

[Anonymous No.10952983]

>>10952965
anon you realise being a quant is one of the best applied maths jobs on the market?
apart from those bullshit calculations that every trading firm asks you for some reason

[Anonymous No.10953011]

>>10952954
>>10952943
>>10952938
Does it help with actually winning at games?

[Anonymous No.10953018]

>>10953011
nope

[Anonymous No.10953029]

Hey, lads. I've signed up for a PhD maths subject this semester, and we essentially go to a room, the professor opens up the book, reads it out loud while explaining the intuition and adding commentary based on his experience. Sometimes he gets stuck and we pitch in.
It's overall extremely comfy.
Is this standard?
>>10952878
>most interesting
Poincaré.
>>10952500
No.

[Anonymous No.10953034]

>>10953011
maybe

[Anonymous No.10953227]

I already started Artin's algebra now you guys are saying Lang is better author. What the fuck man? Has anyone really read the two and know for sure exactly which is more rigorous? I don't care about easy reading but it should give detailed exposition.

[Anonymous No.10953230]

>>10953029
You have to ignore class and group studying. All that matters is self study, specially for Phd.

[Anonymous No.10953249]

This chart has some cool books, the analysis and multivariable ones are pretty great. It made me think about something:
What are the books you guys know about the main math subjects(topology, algebra, linear algebra, analysis, diff geometry,...) that are underrated but you find it really good?

[Anonymous No.10953250]

>>10953011
yes

[Anonymous No.10953257]

>>10953011
doesn't have to be applied to only games, you can consider every situation a 'game' with a winner and a loser, interactions with your wife, friends, children etc. be the WinRAR.

[Anonymous No.10953268]

>>10953249
>Linear algebra
Howard Anton
>Algebra
Artin
>Probability
Sheldon
>Calculus
Anton
>Number Theory
Hardy
>Anal
Tao
>Geometry
Some random thot

[Anonymous No.10953271]

game theory is useless wankery which doesn't help at all when it comes to real world games
prove me wrong

[Anonymous No.10953276]

>>10953271
(((you)))

[Anonymous No.10953290]

>>10953230
I'm not doing a PhD, just the class.
>>10953227
>I don't care about easy reading but it should give detailed exposition.
Read Bourbaki.

[Anonymous No.10953364]

>>10953227
Both are fine. Lang is shorter and more abstract, as far as the lin alg book goes. You're fine off with both.

[Anonymous No.10953483]

>>10953227
>Lang
Lang is a meme.

[Anonymous No.10953947]

>>10953271
Game theory is a bad name desu. It's more about microeconomics than anything

[Anonymous No.10954995]

>>10946255
Has anyone benefited from this ?

[Anonymous No.10955110]

Starting Bourbaki. Should I expect mental breakdown?

[Anonymous No.10955197]

>>10953483
Lang's book on group cohomo is tres bon, though.

[Anonymous No.10955209]

Which math subfield is the nigger of the math world?

[Anonymous No.10955212]

>>10955209
Computer Science or Mathematical Logic

[Anonymous No.10955257]

>>10955209
actually, the whole field of math is a nigger

[Anonymous No.10955293]

>>10955257
//thread

[Anonymous No.10955306]

Is Math the DNA of reality? I think so. Physics is the next macro step IMO. Based Math, you are my god.

[Anonymous No.10955325]

>>10955306
no math is the quarks and algebraic geometry is the atoms

[Anonymous No.10955331]

>>10955325
After consulting with my based Jewish lawyers just now, I'm told "algebraic geometry" is in fact math. So in essence, we are in agreement? If not my lawyers will email you shortly.

[Anonymous No.10955346]

Does the notion notion of "graded" have any restriction w.r.t. how you fractionate a graded vector space?

Example: Polynomials in X and Y as vectors may be considered to live in a graded vector spaces, e.g. with
3 + 2 X + Y - X Y + X^2 Y+ Y^3
breaking into the homgenous parts with subcomponents
3
2 X + Y
- X Y
X^2 Y+ Y^3

But is this essentially arbitrary? For example: Can I also consider a vector space of such polynomials be graded into two where I say one subspaces is polynomials up to order 5 and the other subspace from 5 on. Or any criteria at all that clusters 1 dimensional subspaces?

I'm aware that some homomorphism may only be defined on some subsystems, but is the overall definition of the parts in a graded subspace restricted?

[Anonymous No.10955372]

>>10955346
Yes. The subspaces must be homogeneous, i.e. f(x)=k^n.f(x) for some n.

[Anonymous No.10955433]

what is the solution of |x-1| = 1-x?

I'm trying: (1) x-1 = 1-x when x-1 > 0, so x= 1 when x>1 but that makes no sense, and (2): x-1 = -(1-x) when x-1< 0, so 0x = 0 when x < 1 which makes no sense either, help me,

[Anonymous No.10955439]

>>10955433
very low iq post

[Anonymous No.10955472]

Sharing something I learned from here:
https://web.sonoma.edu/users/w/wilsonst/papers/Normal/default.html

The normal distribution density function is the (unique) solution of the differential equation
f'(x) = - k (x-c) f(x)
under the assumption that f integrates to 1.

c can be proven to be the mean and k to be 1/σ^2

So, it's really the unique distribution density function which drops whenever you are getting away from the mean, in a way that it is proportional to the distance from the mean, as well as the density at that point.

[Anonymous No.10955516]

>>10955439
help me then

[Anonymous No.10955560]

>>10955372
kk, but I'm talking about the general definition (unrelated to polynomials, this was just an example)

[Anonymous No.10955577]

>>10955472
That's nice, "but" it sounds this will work with any function q(x) and
>f'(x) = -q'(x) * f(x)
where left and right of a finite supporting area (i.e. going towards minus and plus infinity), q(x) is eventually positive and grows slower than the exponential falls.
The uniquness is just the uniqueness of well behaved first order ODE's.

[Anonymous No.10955767]

>>10946255
Let's say I have a cylinder whose diameter is 1 unit wide and 2 units long. If we lay this on something hard and flatten it lengthwise, how to calculate the thickness? For example, if I want to end up with a flattened cylinder with a thickness of .25, what thickness of cylinder do I need to start with?

[Anonymous No.10955771]

Is there any reason to use cosets other than to construct a Quotient group?

[Anonymous No.10955804]

>tutoring engineering student
>he doesn't even know how to graph
do engineers really?

[Anonymous No.10955919]

>>10955767
>If we lay this on something hard and flatten it lengthwise, how to calculate the thickness?
What have you tried?

[Anonymous No.10955922]

>>10955804
>engineering
not science or math

[Anonymous No.10955969]

>>10955771
Some combinatorial problems make use of them in a way that doesn't explicitly reference the quotient group.

[Anonymous No.10956024]

>>10955771
Transfer maps, for example. Given a group [math]G[/math] and a subgroup [math]H \le G[/math], one has the map even if [math]H[/math] is not normal, or equivalently [math]G/H[/math] is not a group.

[Anonymous No.10956097]

What area should I go into for my PhD? I'm considering algebraic topology.

[Anonymous No.10956226]

>>10955919
Using my imagination to see the cylinder getting flattened.
Luckily, I found the math. People use it to make a flat rod out of a round one apparently that is what it is called.

[Anonymous No.10956242]

No matter how much I try to rationalize in my head the concept of complex numbers, and the more explanations I read and watch, THEY JUST DON'T MAKE SENSE to me. Where in this universe does the complex plane reside? Is it a hidden dimension or what? Explain like I'm 24 in college majoring in economics.

[Anonymous No.10956250]

>>10955922
cope

[Anonymous No.10956259]

>>10956242
dude it's just 2 dimensions. it's just a plane.
complex numbers are a useful way to write vectors of length 2 because when you multiply them you rotate one by the angle of the other, and you need to do that with vectors a lot.

[Anonymous No.10956260]

>>10956097
Sounds good.

>>10956242
The complex numbers have a representation among GL(2,R), i.e.
a+ib exactly behaves like the matrices ((a,-b),(b,a)) where a,b are in R. So to study C is just studying those matrices, and they fullfil the fundamental theorem of algebra.
(However, justifying whatever setup for R to the extend that you want to embed it in the mathematical world as a whole is another issue.)

[Anonymous No.10956261]

>>10956260
in particular,
((0, -1), (1,0))^2 = -((1,0), (0, 1))

i^2 = -1

[Anonymous No.10956271]

Retard here. How do you prove that sin(θ) is surjective on the complex plane C \ {0}C?

[Anonymous No.10956289]

>>10956259
Let me try to explain one thing that's bothering me. Suppose you have f(x) = x^2+1. The fundamental theorem of algebra says that for this function there should be two x values that make it 0. Now, WHYYYY would you even CARE if this function has roots?? So what, it's not zero anywhere, why the hell should I care? Yes the theorem gives two complex roots, but again, WHY would you care that there aren't real roots?

[Anonymous No.10956360]

>>10956271
It's surjective on the normal complex plane, and sin(0)=sin(2pi).

[Anonymous No.10956416]

>>10956289
Why would you care about anything in life. This is not a hyperbole. Think about the meaning of life for a second.

You probably think math is for applications. Well I don't agree - but if you do, then you have a good argument for complex numbers, they are very useful to calculate stuff such as signal analysis. Always being able to write any polynomial [math]p(x)[/math] of order n as as
[math] p(x) = \prod_{k=1}^n (x-x_i) [/math]
is convenient. And that's the fundamental theorem.

[Anonymous No.10956463]

>>10956289
> Suppose you have f(x) = x^2+1. The fundamental theorem of algebra says that for this function there should be two x values that make it 0. Now, WHYYYY would you even CARE if this function has roots??
So that you can factor it as (x-a)(x-b). Every degree-N polynomial can be factored to k(x-r1)(x-r2)...(x-rN), provided that you allow for the roots being complex. This has practical utility e.g. for decomposing rational functions to partial fractions.

Also: an equation involving only real coefficients and whose solutions are real may be easier to solve if you allow for the possibility of intermediate terms being complex. The best-known example being the solution of cubic polynomials, which is where complex numbers originate. With only real numbers, you have one equation for the case where the cubic has one real root and a completely different equation for the case where it has three real roots. If you allow for intermediate terms being complex, the first equation works for both cases.

[Anonymous No.10956479]

What field of math best combines algebra and analysis.

[Anonymous No.10956485]

>>10956479
I don't even know what analysis is. Is it not just calculus?

[Anonymous No.10956499]

>>10951724
what is this

[Anonymous No.10956501]

Should I drink or it will lower my IQ?

[Anonymous No.10956503]

>>10956501
Fuck rotation.

[Anonymous No.10956505]

>>10956479
Pretty much every application of math does this.
Statistics is a pretty good example.

[Anonymous No.10956506]

>>10955212
Hey, shut up

[Anonymous No.10956507]

>>10956485
It is but you prove the results of calculus and look at estoric function behavior.

[Anonymous No.10956523]

I have a high verbal IQ of 134 and a spacial IQ around 120 but an utterly awful working memory of 84.

Am I gonna make it? I was able to easy get A's in Calc 1 and 2. I just have to compensate by writing everything down. However i'm really good at intuitively understanding things.

[Anonymous No.10956534]

>>10956501
should it be possible

[Anonymous No.10956540]

>>10956501
>wine
pleb taste, only vodka+ percentages are allowed

[Anonymous No.10956564]

>>10956523
>posted anime
nope you're not gonna make it.

[Anonymous No.10956566]

How does one invent a new field in math? Do they start just playing around with new definitions that they made up and see where it goes, do they just play around with some things looking for a pattern and then delving deeper until they can see where it goes?

[Anonymous No.10956577]

>>10956566
Study Hamilton and how he came up with quaternions.

[Anonymous No.10956579]

>>10956479
Number theory or some C* algebra shit

[Anonymous No.10956595]

Do you guys want a function that returns 1 if more or equal to n and 0 if smaller? There's no max, lim, elif etc....

[Anonymous No.10956606]

>>10956595
Basically

F(x) = (|x|+x)/2x

[Anonymous No.10956657]

>>10956479
modular forms
topological groups and their notions of duality transforms

[Anonymous No.10956777]

how do i solve |x-1| = 1-x?

[Anonymous No.10956810]

http://www.bristol.ac.uk/news/2019/september/sum-of-three-cubes-.html

[Anonymous No.10956814]

>>10956777
x-1 = 1-x if x is at least 1 or 1-x=1-x if x is at most 1. The first case gives you x-1 = 1-x <-> 2x = 2 <-> x = 1 (which is ok), and the latter is true for all x at most 1, so the equation holds for any x at most 1.

[Anonymous No.10956828]

>>10947701
It's because you never learned it, you just need to know how to use a graphing calculator

[Anonymous No.10956846]

>>10956814
Yeah, thanks, just found it out too. had to remember way back when i was learning this... so (-infinite,1], right?

[Anonymous No.10956854]

>>10956810
>x^3+y^3+z^3=k
>The answer, which took over a million hours of calculating to prove, is as follows:
>X = -80538738812075974 Y = 80435758145817515 Z = 12602123297335631

what did they mean by this?

[Anonymous No.10956907]

>>10956846
Yup, [math]x \in (- \infty, 1][/math].

[Anonymous No.10956924]

>>10956854
>what did they mean by this?

[Anonymous No.10956991]

>>10948087
I mean I just really dont see this ever being generally true or untrue

[Anonymous No.10957396]

How do I develop the intuition behind Baye's rule?

[Anonymous No.10957404]

>>10957396
>How do I develop the intuition behind Baye's rule?
All reputable statisticians reject Bayes "theorem".

[Anonymous No.10957418]

>>10957404
On what grounds besides autism?

[Anonymous No.10957426]

>>10955516
|x-1|=sqrt[(x-1)^2]
That should give you everything you need

[Anonymous No.10957435]

>>10957396
https://en.wikipedia.org/wiki/Monty_Hall_problem

[Anonymous No.10957452]

Is there a mathematical theorem which proves/suggests that science is faith based?

[Anonymous No.10957458]

>>10957452
>Is there a mathematical theorem which proves/suggests that science is faith based?

[Anonymous No.10957702]

>>10956810
Oh look, another proof by brute force.

[Anonymous No.10957732]

>>10946255
What is your favorite algebra /mg/?

For me, it's Boolean rings.

[Anonymous No.10957769]

How do I show that a set A over the set of real numbers is a vector space?

[Anonymous No.10957776]

>>10957769
>How do I show that a set A over the set of real numbers is a vector space?
What have you tried?

[Anonymous No.10957784]

>>10957732

One time in undergrad algebra we were looking at some structure that had 20 things, and it looked like there were (about) 30 ways that they might relate to each other. So I posted a conjecture on the class' group board: "I bet this thing has a diagram like a docecahedron!"

The conjecture turned out to be (partly) false in the sense that I couldn't fill in all 30 edges truthfully. But I shoehorned a good 20+ mappings into my fun picture.

[Anonymous No.10957786]

I figured out why the formula for picking two objects from a group of 10 objects have the formula 10C2.

[Anonymous No.10957788]

>>10956810
I hate it. You run one supercomputer to do all permutations and yay we found the solution lads.

[Anonymous No.10957791]

Klaus Janich or Munkers?

[Anonymous No.10957794]

>>10957784
20 axioms? What the fuck kind of algebra is that?

[Anonymous No.10957800]

>>10957786
Congratulations, you'll pass business pre-calc

[Anonymous No.10957824]

Too stoned to be sure that I didn't make a mistake in this proof.
Any suggestions will help :)

[Anonymous No.10957842]

>>10957791
Janich if self taught, but still read munkers for formalism.

[Anonymous No.10957883]

>>10957824
Not sure about this one bud, I don't see how your proof shows p->q (you didn't mention how gcd(a,b)=1 anywhere in your proof). IN the line with "by theorem...", you turned a^2 into c^2*k^2 when it should be c*k and the same with b^2, which ruins the next line. In the last line there's an extra | at "c(k^2m+j^2n)|". For this proof personally I would have made an argument using the fact that a and a^2 have the same factors.

[Anonymous No.10957888]

>>10957883
>a and a^2 have the same factors.
yeah

[Anonymous No.10957929]

>>10956991
The claim is false, as it says 4, 9 and 15 are primes, for example.

[Anonymous No.10958078]

Have a question about the order of an automorphism of a finite group: Let [math]G[/math] be a finite group of order [math]n[/math]. Must every automorphism of [math]G[/math] have order less than [math]n[/math]?

[Anonymous No.10958083]

>>10957883
please learn how to use [math] [/math]

[Anonymous No.10958085]

>>10958078
>Must every automorphism of G have order less than n?
What have you tried?

[Anonymous No.10958104]

>>10957732
So we just shove a type together with a structure and it's an algebra? Numerical semigroups are pretty bomb.

[Anonymous No.10958159]

Since I started my PHD a couple of months ago I found quite a few errors in publications. Is this normal?
Also, do you think at some point in the future all mathematicians will have to agree on notation? For example, everyone including me seems to make mistakes because of different sign conventions of the curvature tensor.

[Anonymous No.10958197]

>>10946895
There is an objective answer:
As long as you formally/rigorously define, state and proof things you are doing mathematics. You miggt also be doing engineering or chemistry at the same time though.
What I mean is that math is just formally analyzing structures and coming to 100% true theorems. So if you are a chemist and you for example make a formal definition of what molecular structure counts as an alcohol, and then prove with graph theory soemthing about how many alcohols exist with less than n mass (I only remember a bit of highschool chemistry) then you are doing maths.
But if you just make informal, word heavy arguments which make sense but you could come up with abusrd edge cases that are counterexamples, you are not doing maths.

[Anonymous No.10958244]

>>10957396
It says that the p(x|y), probability for x being observed given y having been observed, is proportional to two things:
* x being observed generally
* the likelihood p(y|x) of your observation observation y in the first place having come from x

Wikipedia gives the following task in pic related, which is a good example (it also states the answer).

If you look at a system that is described by a joint distribution f(x,y) (where f(u, v)/f(a, b) say how much more often u,v is seen together than a, b), then you can normalize (with sum or integral) that f to 1, thus obtain a joint probability and in that case, Bayes rule is actually a provable theorem.
That is, if the the correlations can be statistically sampled before you start using the theorem (e.g. by doing statistically evaluating how often OP is fag, getting hard numbers), then Bayes theorem is, in fancy terms, a straight forward functional analysis result stemming from normalization (sum/integral) being linear.

Whether think Bayes rule about conditional probability is relevant to events without possible statistical data and where you have to pull priors out of your ass ("Will the Queen die next March?") is up to your interpretation of chance.

>>10957732
sl(2,C), su(3)

>>10958159
It will not happen overall, but you can do it if you're influential and opinionated.

>>10958197
That's good willed, but it leaves out the detail that much of research mathematics is not based on axioms - it's dabbling around with should-be relations and the axiomatic is often done in the upcoming decade, where the strong theorems and low hanging famous fruits have already been plugged on relatively speaking informal grounds.
Moreover, logicians and type theorists tend to complain that university mathematics is often leaving out details, even for decades, and in their head do things like identifying x and {x} and isomorphisms like that. There's no limit to formality - until you're a computer.

[Anonymous No.10958254]

How do I force myself to like proofs? Do I ever get used to it? Atm it's really hard to follow

[Anonymous No.10958271]

>>10958254
Why do you find them hard? Since you are asking this, I can make a pretty safe assumption that your proofs are pretty much on the level of [math]1 + 2 + 3 + \cdots + n = \frac{n(n+1)}{2}[/math]. You'll have to do some simple proofs to understand that proving stuff is basically like playing a Pokémon game, but this time you have all the knowledge you possess instead of just the at most 4 moves your Bulbasaur would otherwise have. Then you use those moves (i.e. the results in your material etc.) to attack the opponent (the result you are trying to prove), and the goal is to make your opponent's HP go to 0. If you use an attack strong enough, you can one-hit-KO the opponent, but you can also use weaker attacks to defeat them. For example, you can prove that every non-zero rational number has a multiplicative inverse by arguing that if [math]m, n \in \mathbb{Z} \setminus \{ 0\}[/math], then [math]\frac{m}{n} \in \mathbb{Q} \setminus \{ 0 \}[/math] and [math]\frac{n}{m} \in \mathbb{Q}[/math] is its multiplicative inverse, which is pretty much a super effective critical strike, but you can also use less effective moves like going through all the field axioms one by one and showing that the rational numbers satisfy those. Essentially, might makes right. Proving is all about power relations between results, and the strong ones lead to the weaker ones.

[Anonymous No.10958320]

>>10958271
Well, i'm not talking about -that- easy proofs. I'm talking about proofs in analysis/calc with epsilon and delta, sup, min/max shit and also more in number theory that goes beyond mathematical induction. I find them hard usually because I have no idea where to start and what to do, but once I see the solutions they seem easy af - and so I question myself why I couldnt to them myself

[Anonymous No.10958345]

>>10958320
How I did those epsilon thingies was that I took the function or sequence and whatever it was supposed to converge to, and set their absolute difference less than or equal to epsilon. Then I untangled it to get a suitable threshold index or delta to reach the desired conclusion. Try that. Like, for example [math](x_n)_{n \in \mathbb{N}}[/math] with [math]x_n = \frac{1}{n+1}[/math], and I want to show that this converges to 0. I take my [math]\varepsilon > 0[/math], set [math]x_N \le \varepsilon \Leftrightarrow \frac{1}{1+N} \le \varepsilon \Leftrightarrow 1 \le \varepsilon + N\varepsilon \Leftrightarrow N \ge \frac{1 - \varepsilon}{\varepsilon} [/math]. Now, if [math]n > \frac{1 - \varepsilon}{\varepsilon}[/math], then [math]x_n < \varepsilon[/math], so [math]x_n \to 0[/math] when [math]n \to \infty[/math]. Try to develop the same idea for functions and epsilon-delta.

[Anonymous No.10958398]

>>10958254
I read this as
>how do I force myself to like Profs?

[Anonymous No.10958417]

>>10958078
>https://en.wikipedia.org/wiki/Monty_Hall_problem
Not sure about outer automorphisms, but for inner automorphisms, i.e. conjugation, their order must be a divisor of n

[Anonymous No.10958419]

>>10958417
ignore monty hall

[Anonymous No.10958421]

>>10946255
No other subject other than probability(specially problems involving counting number of combination etc) fuck with intuition so much. Prove me wrong.

[Anonymous No.10958434]

>>10958419
no, I like that post like that

>>10958421
If you speak about things like the birthday problem, I'm spontaneously inclined to agree. However, it must be pointed out that this may be due to number theory being one of the few math things that are accessible early one - i.e. you actually have intuitions about quantity relations early on. Of course, algebraic groups don't fuck with your intuition too much, since even if you'd find the results surprising, you don't actually have great intuitions about what the results would or could be from the get go.

Pic also related.
Side-note: I'm reading into this Algebraic Groups book and it's 600 pages where they enumerate every fucking paragraph like they are Wittgenstein or the Bible or something. Not sure what I think about that. I suppose it can be helpful, but it makes the layout quite aggressive to look at.

[Anonymous No.10958436]

>>10958419
>>10958417
I think you're looking at the wrong Hall https://en.wikipedia.org/wiki/Hall%27s_universal_group

>>10958078

[Anonymous No.10958446]

From monday the price of a TV was reduced by 20% in a sale. On Wednesday the TV was reduced by a further 10% Alan bought the TV on Wednesday for £604.80. What was the price of the TV before the sale?

[Anonymous No.10958454]

>>10958446
/mg/ is a PhD-level thread anon. I'm kindly asking you to post this elsewhere, preferably on /r9k/ or /b/. Thanks a lot.

[Anonymous No.10958455]

>>10958446
604.80 = 0.9*0.8*P <-> P = 604.80/(0.9*0.8)

[Anonymous No.10958462]

>>10958454
kek

[Anonymous No.10958463]

>>10958454
Ok sorry
>>10958455
Thanks very much :)

[Anonymous No.10958465]

>>10958345
Okay, thanks

[Anonymous No.10958478]

>>10958434
I remember some of algebra. GLn is General Linear Group is it?
Don't know what SL is.
I am following this. Want to finish 2 chapters today. It's challenging to digest things.

[Anonymous No.10958485]

>>10958478
>Don't know what SL is.
GL with the condition determinant = 1.

[Anonymous No.10958675]

I always fail to answer question like this. How do I make this intuitive to me? Just like I can say 1+1=2.
>Given group of n objects, how many different subgroups of r can be made with a condition that no group has two(in general m objects) special objects that cannot be present in one group.
Can anyone reply without referring anything?

[Anonymous No.10958735]

>>10957396
literally just draw a bunch of prob trees for different examples, worked for me

[Anonymous No.10958891]

>>10958675
Do you mean that you have m fixed objects that cannot belong to one subgroup ?
It simply means that you are forming your groups by choosing r elements out of the remaining n-m, hence the total number of distinct such subgroups is [math]{n-m \choose r}[/math]

[Anonymous No.10959028]

What's a good parametrization of points in an equilateral triangle, for the sake of computing the point distance from each of the triangle points?

One could use two of the distances as parametrizations, but then what is the third distance? Not sure if that proposal is a good one anyway.

[Anonymous No.10959178]

>>10956523
>mentions iq
no, you're not gonna make it

[Anonymous No.10959409]

>>10956523
>cares about grades
negatory, you're not gonna make it

[Anonymous No.10959458]

Is the determinant trick for cross products just a coincidence or is there a deeper connection between the two??

[Anonymous No.10959472]

>>10959458
https://en.wikipedia.org/wiki/Exterior_algebra#Linear_algebra

[Anonymous No.10959664]

What is the largest dimension of a subspace of [math]n \times n[/math] Hermitian matrices which does NOT contain a rank-one positive semidefinite matrix?

[Anonymous No.10959733]

>>10957458
That is pure nonsense.

[Anonymous No.10959734]

>>10959458
The definition of cross product [math]u\times v[/math] is that it's the unique vector satisfying [math]<u\times v,w> = \det(u,v,w)[/math] for every vector [math]w[/math]. From this you get all geometric and algebraic properties.

[Anonymous No.10959800]

For a person who failed grade 10 math, I did ok.

[Anonymous No.10959806]

>>10959664
>What is the largest dimension of a subspace of [math]n \times n[/math] Hermitian matrices which does NOT contain a rank-one positive semidefinite matrix?
What have you tried?

[Anonymous No.10959857]

>>10959664
Have you tried computing the dimension of the space spanned by rank one positive semidefinite matrices and then subtracting it from n^2?

[Anonymous No.10959918]

What would be the implications if I discovered a P algorithm for finding the minimum bandwidth of a sparse matrix/graph?

[Anonymous No.10961253]

>>10959918
The trivial approach is O(n^2), so literally nothing.

[Anonymous No.10961284]

>>10961253
I thought it was NP-complete. Source?

[Anonymous No.10961304]

>>10961284
>I thought it was NP-complete.
There are n^2 elements in a matrix going through all of them and computing the difference of their indices for all on zero entries and the computing the minimum is the trivial, polynomial, algorithm for computing the bandwidth of a matrix.

Depending on the storage format there might even be faster algorithms.

[Anonymous No.10961341]

>>10961304
When I discover that fucking Sergei has set the wave function after drinking and without a reference

[Anonymous No.10961345]

>>10961341
What the fuck are you on about?

[Anonymous No.10961371]

is (X_n)_(n >= 1) = (n)_(n>=1) restricted from below or not? I mean Xn cannot be < 1, but still

[Anonymous No.10961372]

>>10961304
That's computing the bandwidth, not finding the permutation of the matrix with the minimum bandwidth. Finding a minimal bandwidth permutation is currently thought to be NP-complete.

[Anonymous No.10961374]

>>10961372
>That's computing the bandwidth, not finding the permutation of the matrix with the minimum bandwidth.
Obviously. That was asked in >>10959918.

[Anonymous No.10961378]

>>10961374
>>10959918
>finding the minimum bandwidth
>minimum bandwidth
>minimum
>m
>i
>n
>i
>m
>u
>m

[Anonymous No.10961384]

>>10961378
A Matrix has exactly one bandwidth, that bandwidth is the minimum bandwidth.

[Anonymous No.10961387]

>>10961384
No, you are incorrect. See https://en.wikipedia.org/wiki/Cuthill%E2%80%93McKee_algorithm

[Anonymous No.10961398]

>>10961387
>No, you are incorrect.
???
What the fuck.
A Matrix has a unique (upper) bandwidth which is also its minimum bandwidth, that can be computed in polynomial time.
That is a fact.

A matrix CAN also be permuted INTO ANOTHER MATRIX with a different Bandwidth, but that anybody was concerned with permutations was first mentioned in >>10961372.

[Anonymous No.10961403]

>>10961398
yikes

[Anonymous No.10961413]

>>10961403
Please laugh at yourself, the person who claims that a matrix can have multiple bandwidths...

[Anonymous No.10961415]

>>10961413
You are a retard. This a major problem in numerical linear algebra and graph theory.

[Anonymous No.10961420]

>>10961415
>This a major problem in numerical linear algebra and graph theory.
No, computing the Bandwidth of a Matrix isn't a serious problem.

[Anonymous No.10961465]

Can I get some help? How do I find sup and inf of a sequence? like, what is the "method"?

[Anonymous No.10961482]

>>10961420
An efficient algorithm for finding minimal bandwidth permutations would allow you to trivially solve large sparse problems. Dumbass.

[Anonymous No.10961486]

>>10961482
>An efficient algorithm for finding minimal bandwidth permutations would allow you to trivially solve large sparse problems.
Yes. But why do you keep bringing up permutations when they had nothing to do with the original topic?

[Anonymous No.10961488]

>>10961465
There is no "method".

[Anonymous No.10961498]

>>10961488
>>10961465
there actually is a method and it's simpler than you think

START PAYING ATTENTION AND GO READ A BOOK RETARD

[Anonymous No.10961506]

>>10961486
That was the original topic when I posted it. You are just coping.

[Anonymous No.10961516]

>>10961498
wow, thanks!

[Anonymous No.10961567]

>>10961506
>That was the original topic when I posted it.
Nope.
There was no mention of permutations anywhere.

[Anonymous No.10961886]

>>10961567
It's your fault for being a brainlet.

https://stackoverflow.com/questions/5616605/minimum-bandwidth-problem

[Anonymous No.10961924]

If f has

[math] \forall n. \forall m.\ m > n \implies |f(m)-f(n)| < b^{-n} [/math]

and g has

[math] \forall n. \ |g(n)-f(n)| < b^{-n} [/math]

does this imply g also has the first property?
The first property says, roughly, the digits compute quickly and the second that g is exceedingly close to f.

[Anonymous No.10962243]

>>10957776
Can I use this?

[Anonymous No.10962549]

>>10962243
It doens't sound like you start with a vector space (of which you'd consider a subset), do you? Sounds more like A builds the basis (vectors)? I might be wrong.

>>10961924
Btw. in both cases here I meant not that it holds for all n, but that it eventually holds for all n. I don't care about the initial segment.

[Anonymous No.10962760]

>>10962243
No, you want to show that the entire set is a vector space. Just verify that there is closure under addition and scalar multiplication and that there exists an additive identity element. Verifying the other axioms is a much more trivial matter.