/sci/ - Science & Math

What's 1+1?

>>11861587
it's window innit

>>11861587
3

>>11861585
>Elliptic curves

>>11861587
0 (mod 2)

>>11861601
spamming the same thing in each thread is retarded and you'll eventually get tired of it. See the "threadly reminder to work with physicists" guy? Yeah me neither.

>>11861625
I like those guy's recurring posts and I see the physicist guy every now and them. Either way I'm sure he posted it for many years, you don't really make a strong case there

>>11861641
Up until recently he posted it in every thread. He moved on now.

>>11861625
What do you have against elliptic curves, anon?

>>11861648
Don't get me wrong, elliptic curves and geometry in general is one of my favourite fields of maths.
I just don't like spamming.

>Teaching degree, first year
>Have to study a math textbook from another country, grades 8 to 12
>Analyse and describe the writing style and flaws, six page paper
>Zambia, grade 11
>Only one or two typoes per 5 pages, no math typoes
>English is perfectly comprehensible
>Unit 1: Approximation
>Too much intro stuff about learning aims, only a few problems per subsection, otherwise fine, clearly meant for classroom use.
>Unit 1 Topic 2: Standard form
>Explanation is pretty good except it uses set notation for no reason, the indexes don't mention anything else to do with sets in the whole book, just this tiny section
>Example problem 1:
>Supposing the number of students infected with HIV at a certain college makes up two thirds of the student population. If there are 1 680 students infected with HIV at the college, how many students are there at the college altogether? Express your answer in standard form.
Is this a math textbook or a current affairs textbook?

Prove that any open set in $\R$ can be written as the union of at most countably many disjoint open intervals.
\begin{proof}
Let $U\subset\R$ be open. If $U=\emptyset$ there is nothing to prove, so suppose $U$ is nonempty and let $x\in U$.

If $x\in\Q\cap U$, since $U$ is open there exists an open interval $I$ containing $x$. Let $\{I_\alpha\}_{\alpha\in A}$ be the family of open
intervals in $U$ containing $x$, which we know is nonempty. Here, $A$ is simply an arbitrary indexing set of unknown cardinality. Define $I_x := \bigcup_{\alpha\in A}I_{\alpha}$ to be the open interval obtained by the union of $\{I_{\alpha}\}_{\alpha\in A}$. We know $I_x$ is open
because it is the union of open intervals, and we know $I_x$ is an interval because $x\in\bigcap_{\alpha\in A} I_{\alpha}\implies \bigcap_{\alpha\in A} I_{\alpha} \neq \emptyset$, i.e. $I_x$ is connected.

If $x\in \Q^c\cap U$, then since $U$ is open there exists an open interal $J\subset U$ such that $x\in J$. By the denseness of $\Q$ in $\R$ we
know there exists $y\in J$, and by construction this means $J\subset I_y$. Therefore, for every $x\in U$ there exists $y\in\Q$, where it is
possible $y=x$, such that $x\in I_y$. Since $x\in U$ this means
$$
U\subset\bigcup_{y\in \Q\cap U} I_y
$$
and since $I_y\subset U$ we have
$$
\bigcup_{y\in \Q\cap U} I_y \subset U \implies U = \bigcup_{y\in \Q\cap U} I_y
$$
and since $\Q$ is countable we know this is a countable union. It suffices to show that each $I_y$ is pairwise disjoint from another. If $x\in I_q\cap I_p$ with $p\neq q$, then since $I_q$ and $I_p$ are open intervals containing $x$, their union is an open interval. Therefore by construction we have $I_p\cup I_q\subset I_p$ and $I_p\cup I_q\subset I_q$, i.e., $I_p = I_p\cup I_q = I_q$, so $I_p = I_q$. Therefore by the contrapositive we have if $I_p\neq I_q$ then $I_p\cap I_q = \emptyset$, i.e., the intervals are parwise disjoint.
\end{proof}

Sorry for reposting. I asked right before the new thread was made.
I'm reading A New Introduction to Modal Logic from Hughes & Cresswell, and I'm pretty stuck on modal predicate logic. While I could mostly understand modal propositional logic, I'm having much more issues with this. Some proofs are 10 pages long and it makes me want to kill myself. Are there any other books you recommend instead?

>>11861656
mate this is /sci/ we use [math] [/math] here and [eqn] [/eqn]

>>11861656

>>11861656
TIME TO GO BACK.

>>11861645
physics guy and yukari and /gnmg/ anon have all moved on, what's even the point of it all? Why are we still here? Just to suffer?

>>11861625
Upvoted

>>11861712
>oh no what will happen now that the annoying attention whoring shitposters are gone!

>>11861656
cringe post, based picture tho

>>11861712
We're still here because we don't really have anything better to do.
Also, blond anime girl anon whose name I don't know is probably still here and I like him.

>>11861666
[eqn]\mathfrak{KeK}[/eqn]

>>11861723
>blond anime girl anon
who was that?

>>11861739
This guy: >>/sci/thread/S11829106#p11833064

>>11861723
>>11861739
Collette.

>>11861712
>/gnmg/ anon
Still here.

>>11861768
>Still here.
That's great to hear

>>11861773
Merci. Is it summer break over there or have you been making progress with your stuff?

>>11861782
It's summer, so I'm taking my little break before next year kills me. (though I'm prestudying so I will hopefully have a better time.) 7/8 of my classes are gonna be math. What about you?

>>11861800
>It's summer, so I'm taking my little break before next year kills me. (though I'm prestudying so I will hopefully have a better time.) 7/8 of my classes are gonna be math.
It's good to have a little break every now and then (yeah yeah NGMI if you need breaks etc). Do you know what sort of stuff your next semester will be full of?
>What about you?
Tried to study a certain space for like 2 months developing all sorts of approaches and always running to a dead end. Now my supervisor and I decided well put that side project to a pause and he told me to write a survey of what I have thus far so he can see if there's anything worth publishing. Also trying to fill all sorts of forms so that they don't throw me out of the country because of Brexit.

>>11861825
>Do you know what sort of stuff your next semester will be full of
First semester is Algebra 2, Real analysis 2, intro to topology and ODEs (luckily my uni isn't great so the algebra and ra tracks are pretty slow, algebra is: Basic structure theory of groups, integral domains and field extensions and ra is: Functions of bounded variation, Riemann-Stietjes integration and Lebesgue integration so hopefully not awful. + I'm really excited for topology). Then in January it's gonna be Number theory 1 (got behind on that one but at least it'll be easier) algebra 3 and (probably) algebraic topology.
>Now my supervisor and I decided well put that side project to a pause and he told me to write a survey of what I have thus far so he can see if there's anything worth publishing
That's always the trouble with research. I hope that you find the gold nugget in the work that you did!
>so that they don't throw me out of the country
Are you at the end of your degree? Surely they wouldn't kick you out halfway through!? Hmm, uncertain times likes this can be very difficult, I hope the bureaucracy moves quick and in your favour!

>>11861852
>algebra is: Basic structure theory of groups, integral domains and field extensions
No Lie theory?

>>11861864
Nope, and none in algebra 3 or the grad level courses (advanced group theory, rings and modules and algebraic geometry), or at least as far as I can tell

>>11861877
Here they are:
>Algebra 3
More structure theory of groups, general ring theory, fields and field extensions, Galois theory.
>Advanced group theory:
Representation theory of finite groups, presentations of finite and infinite groups, or other topics.
>Rings and modules
The general theory of (non-commutative) rings, modules and algebras.
>Algebraic geometry
This course will introduce students to the basics of affine and projective varieties through a combination of basic theoretical tools and elementary examples.

>>11861852
Okay so I would assume the algebra thing is pretty easy if you just put in some effort, ODEs will probably be a mix of messy computations and some results like existence & uniqueness , tolerable. Topology could be general stuff or metric stuff. If it's general, it will be full of definitions that look awfully similar, so watch out for that, and if it's the metric thing, then you will be playing with balls for a while. Algebra 3 and algebraic topology sound good, I hope you get to those. Then you get to do all sorts of homo stuff. Oh and suppose you were to take AT, make sure you know your quotient groups and polynomials before that - and, if possible, exterior algebras and tensor products. What I suggest you do now is maybe prove stuff like how taking the preimage commutes with unions, intersections and complements, how de Moran's laws work and such. Those will make topology a lot easier, this you can trust me on.
>That's always the trouble with research. I hope that you find the gold nugget in the work that you did!
Thanks! I have like 30 pages, so I would assume there is at least something to send somewhere.
>Are you at the end of your degree? Surely they wouldn't kick you out halfway through!? Hmm, uncertain times likes this can be very difficult, I hope the bureaucracy moves quick and in your favour!
I've been here for almost a year now and I have funding for 3 years. I just came in as a "citizen" and now that they left the Union I have become a proper foreigner. It's probably not too much of an effort to actually get it done, but I just can't find the energy to start it. Important and interesting things hardly ever coincide. Anyway, still alive and even sober nowadays, so I guess I'm getting back in to the game.

>complete [math]CAT(k)[/math] spaces

Why is there so much anime here. I'm here to discuss maths, not your childish chinese cartoons. Lame.

>>11861901
Topology will be Munkres 2-5 (I think), all the metric stuff was done in real analysis 1 through Rudin (oof). AT was 1. Homotopy Theory: Fundamental Groups, Homotopically Equivalent Spaces.
2. Group Theory: Presentations, Free Products, Free Products with Amalgamation.
3. The Seifert-Van Kampen Theorem: Computing Fundamental Groups of Spaces.
4. Covering Spaces: Covering Spaces, Covering Groups
5. Classification of coverings: Universal Coverings, Classification Theorems (time permitting)
6. Singular Homology (time permitting but unlikely).
And I assume it will be the same. Thanks for the suggestions.
>so I would assume there is at least something to send somewhere
That's good to hear, be proud of your hard work
>so I would assume there is at least something to send somewhere
Hmm very true
>Anyway, still alive and even sober nowadays, so I guess I'm getting back in to the game.
You love to see it

>>11861934
math is inherently anime

>>11861934
Anime is inherently mathematical.

Consider a metric space with [math]B(x, \epsilon)[/math] denoting the [math]\epsilon[/math]-ball around a point.

Do I need to assume anything special about a function [math]f[/math] so that the limit [eqn]\lim_{\epsilon \to 0} \inf_{x' \in B(x,\epsilon)} f(x')[/eqn] exists for every point [math]x[/math]?

>>11861953
Yeah, you can imagine some weird shit happening where no matter how small a ball you pick there are arbitrarily small points inside.
I imagine you'd be fine if f was bounded below or continuous but you want to check that.

>>11861768
>Collette
Thanks for informing me.
>>11861953
If the function [math]F( \epsilon ) = \inf _{x' \in B(x, \epsilon)} f( x')[/math] exists, it's monotonic, and it's bounded above by [math]f(x)[/math], so it has a right limit at [math]0[/math].

why can't anime girls be real

>>11861934
Every single one of those posts contained more maths than yours. Lucky for you, I'll stop here.

>>11861936
For algebra, maybe recap matrix multiplication to get a way to easily find examples of non-commutative groups and rings. If you know your partitions and equivalence relations (and how they coincide), then there's not much to do as preparation for that. If you want to look at categorical stuff, I recommend seeing the algebraic and topological examples first. For example, one would assume that in a category where the morphisms are functions of some sort, epimorphisms are the surjections. Well, if one considers the full subcategory of Hausdorff spaces, then it is not the case. If this sounds like total gibberish to you at the moment, worry not. It will make sense to you after you survive the topology course, and it is also a reason why the undergrad category theorist meme is grounded in reality. However, you will learn that stuff when you get to AT, so don't rush. I hope you get to at least the fifth stage.
>That's good to hear, be proud of your hard work
Thanks. Trying my best.

>>11861968
No problem.

Anyway, it's getting late, so /gnmg/ and a little exercise for those who need something to do:
Prove that the inclusion [math]\mathbb{Q} \to \mathbb{R}[/math] is an epimorphism in the category of Hausdorff spaces.

>>11861953
>>11861967
As an example of consider a function [math] \mathbb{R} \rightarrow \mathbb{R} [/math] defined as follows:
At the points 1, 1/2, 1/4, 1/8... the function has value 0.
In each of these intervals we choose a sequence of points and make the function unbounded below on this sequence.
Everywhere else the function can be zero as well.

Is this book any good? I'm specifically looking for a book on Lie theory that doesn't assume much differential geometry knowledge.

>>11861976
Goodnight, Hausdorffanon.

>>11861976
good night!

>>11861967
Actually you can show continuity isn't enough.
Exercise: Construct a continuous function on the rationals which is unbounded in any neighbourhood of a point.

>>11861998
Let [math]f[/math] be continuous. Set [math]\delta = 1[/math]. Then there's some [math]\epsilon[/math] such that [math]|x-x'| < \epsilon \rightarrow |f(x)-f(x')|<1 \rightarrow f(x')>f(x)-1 ~ and ~ f(x') < f(x)+1[/math], so it's locally bounded.

>>11862013
Yeah nevermind I'm retarded.

what is the smallest possible values for x,y,z to this if you had any real instead of 4.
i think that this should be much easier but i still can't get my head around it

>>11862066
That would just require minimising a multivariate function, no?

[math]Find \ all \ ordered \ pairs \ (\alpha,\beta)\in \mathbb{N}^2,such \ that \ \frac{1}{\alpha}+\frac{1}{\beta}=\frac{3}{2018}[/math].

Aight, Im a senior year math UG. I want to take PDE and intro to numerical analysis before leaving, and my only opportunity to do that before graduating is this summer 5 week 2 semester, beginning in a few days. I'm an A student in all math classes thus far, we use haberman for pde and sauer for num analysis. The professor says he's had kids take both classes at the same time and get As in both, I'm an autist with no job or kids, so does doing these 2 courses in 5 weeks sound like an overload?

>>11862443
i'd say do it unless you have anything else going on. those are both applied courses at my uni so they can't be too hard

>>11862459
Ye that's why I want to take em. They are both applied, taught by this cool ass physics professor, whereas if I wait to take them next semester intro to num analysis is taught by a literal 1st year postdoc from china and pde by a just not very good or interesting professor. Thank you for the reply!

>>11862443
Is the professor Master Roshi?

>>11862468
that's not "master roshi" that is Sheikh Rasheed

>>11861983
I haven't read it but I know Hall's "Quantum Theory for Mathematicians" so my guess would be yes. Should be of high educational value. Also study some DG, you will be happy one day that you did.

>>11862519
it's crazy how nice it is to have some dg under your belt. i hated it when I was taking the class but it's been super helpful moving forward

>>11862066
[math]
\frac{154476802108746166441951315019919837485664325669565431700026634898253202035277999}{36875131794129999827197811565225474825492979968971970996283137471637224634055579+4373612677928697257861252602371390152816537558161613618621437993378423467772036} \\ + \\
\frac{36875131794129999827197811565225474825492979968971970996283137471637224634055579}{154476802108746166441951315019919837485664325669565431700026634898253202035277999+4373612677928697257861252602371390152816537558161613618621437993378423467772036} \\ + \\
\frac{4373612677928697257861252602371390152816537558161613618621437993378423467772036}
{154476802108746166441951315019919837485664325669565431700026634898253202035277999+36875131794129999827197811565225474825492979968971970996283137471637224634055579} \\ =4
[/math]

https://www.quora.com/How-do-you-find-the-positive-integer-solutions-to-frac-x-y+z-+-frac-y-z+x-+-frac-z-x+y-4

>>11861723
thanks for the warm words
i'm here most of the time, but i rarely attach this anime girl to my posts (since i have only ~40 pictures of her)

>>11862200
multiply by [math]3 \cdot 2018 \alpha \beta[/math], you get
[math]3\cdot 2018 (\alpha + \beta) = 9 \alpha \beta[/math], move shit around,
[math]2018^2 = (3\alpha-2018)(3\beta-2018)[/math]
now just check all the possible factorizations of 2018^2 to finish the exercise

>>11862878
Good post.

Mathbros... I, a CSchad, kneel.

>>11862878
>https://www.quora.com/How-do-you-find-the-positive-integer-solutions-to-frac-x-y+z-+-frac-y-z+x-+-frac-z-x+y-4
Great read.

>>11862878
>>11863246
>a quora answer that isn't pajeets ranting for 3 paragraphs about something that doesn't answer the question
what the fug is happening

>>11862879
Get a bigger folder.

>>11862066
i love this shitpost

>>11863326
>shitpost

>>11863323
Removed the background for the sake of it.

>>11863332
good effort

>>11861970
they can be

Tried Modafinil, not really sure why people use it. It doesn't really make you focused. It just makes you feel like you're focused, without any of the perks of really being focused. If you gotta take drugs, it's much better to take painkillers to stop the neck pain.

Love taxicab geometry, lads.

>>11863323
>>11863332
that's a nice picture

>>11863408
i heard it's being superseded by uber geometry, though

>>11863428
What is uber geometry?

I found a bulletin board where you can talk with people all over the world
This bulletin board has automatic translation function


Babelerr

>>11863430
uber, the company which provides a taxi-like service
i was making a poor joke...

Can someone please give me a quick rundown on divisors? I simply do NOT understand what the fuck they are all about. Preferably related to divisors on an algebraic variety, but other types are ok too.

>>11863453
I feel dumb now.

is there any rational trigonometer ITT?

[math]x^3+y^3-3\mu xy=0,\mu \in \mathbb{R}[/math]

Is there any way to find a series expansion for
[math] \dfrac{1}{1-z} [/math]
of the form
[math] \sum_{k=0}^\infty a_k z^k [/math],

converging on some patch outside of the unit disk in the complex numbers?

Emphasis on all k being in {0,1,2,...} and not negative.

>>11863642
Have you considered, get this, Taylor expanding around somewhere other than zero?

>>11863642
This image is photoshopped, notice the king.

>>11863664
I saw this comment before although I wouldn't know what's shopped about the image in total. Maybe it's just a tilted king?

>>11863651
Well yes but I want it in z^k

[math] \dfrac{1}{1-z} = \sum_{k=0}^\infty \dfrac{1}{k!} \dfrac{k!}{(1-p)^k} (p-z)^k = \sum_{k=0}^\infty \dfrac{1}{(1-p)^k} \sum_{j=0}^{k-1} {k \choose j} p^(k-j) \, (-z)^j = \dots [/math]

and then some reshuffling tricks..

>>11863696
>Well yes but I want it in z^k
Bro a power series of the form [math]\sum _{k=0}^{\infty} a_k z^k[/math] either converges around some neighborhood of zero or it doesn't converge anywhere. That's how convergence radii work.
And if it does converge somewhere around zero, it automatically equals [math]\sum _{k=0}^{\infty} z^k[/math]

>>11863710
>Bro a power series of the form ∑∞k=0akzk∑k=0∞akzk either converges around some neighborhood of zero or it doesn't converge anywhere
Okay, I'll take that at face value.
Does this result have a name?

>>11863213
>CSchad
imagine saying this even in jest, just lol at you and your whole race of pencil necked dweebs

>>11863735
This.

>>11863727
https://en.wikipedia.org/wiki/Cauchy%E2%80%93Hadamard_theorem
This one gives the radius of convergence and guarantees that the function converges inside of it.
Checking that it doesn't converge outside of the radius is just a matter of noticing that the terms in the series literally don't converge to zero, so that the series can't fucking converge.

>>11861712
We still have remiliafag, right?

[math]S^1 \times S^1 = T^2 \\ S^1 \times T^2=T^3[/math]

>>11863759
I'm still here.

>>11863740
Okay,
given a sequence [math] (a_k)_k [/math], this tells me how to compute the radius of convergence of
[math] \sum_{k=0}^\infty a_k (z-0)^k [/math]
around the point a=0.
As stated on that site, if the k'th root of [math] a_k [/math] in the limit diverge, then the series doesn't converge _near_ a=0.
>so that the series can't fucking converge.
It says they don't converge around 'a'.

While I'm confident you're correct, I'm unsure if this theorem can be used to argue that a series of the form, which doesn't converge near a=0, can't possibly have a value outside of another point p!=0 around it doesn't converge.

Couldn't there be a patch U somewhere out there up on the complex plane, so that the series [math] \sum_{k=0}^\infty a_k z^k [/math], while not converging around small z, is such that in the patch U there's cancelation of values and it converges?

>>11861712
You have to make it meaningful for them to contribute. Not everyone can just do this forever.

>>11863772
if a series of the form [math]\sum a_k z^k[/math] has a radius of convergence r, then
- for |z|<r, the series converge
- for |z|=r, it depends
- for |z|>r, the series diverge

>>11863794
Isn't that just d'Alembert's ratio test?

>>11863771
then not all is lost

>>11863802
That test doesn't seem to imply that. The test for the series diverging somewhere is conditional on the ratio of sequential coefficient.

Again, I see no reasons why the "a series of this form can only converge on a circle around 0" shouldn't be true, but I also see no proof for it.

>>11863772
Alright, I'll just post a full proof.
Assume that [math]\sum_{k=0}^{\infty} a_k z^k [/math] converges for a fixed [math]z[/math].
Then [math]\lim \sup | a_k z^k | = 0[/math], so [math] \lim \sup | a_k^{1/k} || z | \leq 1[/math], and by swapping in the definition we have from Cauchy-Hadamard we get [math] |z|/R \leq 1[/math].
>>11863771
Based and Remiliapilled.

>>11863835
Okay, I guess I believe it.

>>11863854
Alright, alright, I'll fill in the gap.
If [math]\lim \sup |a_kz^k| = 0 [/math], there exists an [math]N[/math] such that [math] k > N[/math] implies that [math]|a_k z^k| < 1[/math]. Then [math]|a_k z^k|^{1/k} = |a_k^{1/k}| ~ |z| < 1^{1/k} = 1[/math], because the k-th root function is strictly monotonic in the real unit interval [math][0, 1][/math]. Because [math]|a_k ^{1/k} | ~ |z| < 1[/math] for all [math]k > N[/math], we have that [math]\lim \sup |a_k ^{1/k} | |z| \leq 1[/math].

How tough these MIR books are? I'm able to solve them going through Gelfand or Lang's books?

>>11863889

I'm learning Math from the start again as an adult. What's the correct progression path to take on Khan Academy?

>>11862860
To be fair it's really easy for a DG course to turn out bad. If it's a one semester course you need to first ensure that all students are able to deal with sumanifold stuff in [math]\mathbb{R}^n[/math], and then go over to coordinate free stuff. Only after that you can start with the actual nice stuff like curvature. In comparison, courses like complex analysis are a lot easier to teach in a good educational way.

I'm learning Math from the start again as an adult. Which anime should I watch first?

>>11863889
>>11863895
no one can tell you whether you will be able to solve them, because we don't know how good you are
i also suspect that no one here knows the contents of random russian books either

>>11863921
K-On!

>>11863921
Ahiru no Sora if you're physically inclined, Keep Your Hands Off Eizouken otherwise

>>11862878
i know this answer. i'm asking whether it would be easier of you had any integer instead of 4

>>11863912
You're not going to learn math from watching videos go read a book

>>11863977
Which book would you recommend?

>>11863921
Steins; Gate

>>11863980
read the fucking sticky

>>11863986
The sticky has mostly advanced mathematics sources and the one place I found something about beginner related mathematics has a suggestion about using khanacademy.

p-please... someone explain weil divisors....

Bros, I can't even get angry at the author, this is exactly the kind of stupid mistake I'd make.

>>11864015
Where's the mistake?

>>11863999
fucking idiot, wasted trips

[math]v,\nu \\ p,\rho \\ k,\kappa \\ i,\iota \\ w,\omega \\ o,\omicron \\ u, \upsilon[/math]

>>11864037
all easily distinguishable

>>11863999
>>11863912
Arithmetic -> Pre-algebra -> Algebra -> Geometry -> Algebra II/Trigonometry -> Pre-calculus -> Differential calculus -> Integral calculus

>>11864037
most of the problems with distinguishing these stem from poor handwriting/people never being taught how to write the greek symbols properly

>>11864037
in a printed text, easily distinguishable
in your own writing, also easily distinguishable, but you must teach yourself to write those in consistent manner

>>11864059
You can actually distinguish between o and omicron?

>>11864118
Yes.

>>11864118
i admit this one is retarded and i can't distinguish
i don't care though since i haven't seen omicron occuring in a mathematical text ever in my life
but wait... what if all those [math]o[/math]'s were actually [math]\omicron[/math]'s and i never realized...

>>11864127
>>11864141
Alright, I've just double checked by zooming the fuck in like a retard, and the LaTeX used in /sci/ doesn't actually have two different symbols for o and omicron.

>>11864149
The absolute state.
According to Wikipedia, capital omicron was used for Big O notation, but phased out because it was indistinguishable from the capital o in Latin.

>>11864159
>The big-O originally stands for "order of" ("Ordnung", Bachmann 1894), and is thus a Latin letter. Neither Bachmann nor Landau ever call it "Omicron". The symbol was much later on (1976) viewed by Knuth as a capital omicron,[19] probably in reference to his definition of the symbol Omega.
From wiki

Reminder that omikron is the short O and omega is the long one, and should be pronounced awwmega.

Does anime really make you good at math? I asked one of my professors if he watches anime and he seemed unsettled but dodged the question.

>>11864300
lmao, he definitely watches anime, but no, it doesn't make you good at math.

A short book on spherical geometry? Nothing too deep, just for understanding fundamentals.

>>11863642
>tfw no botez gf to play chess with and she beats you every time at first but you easily catch up to her because of your superior male brain and then have kids

>>11863913
i just didn't like do carmo. the class would have been way better off using spivak's pirate book but it's so deeply out of print that I can't imagine it would have been okayed by the dept (even though everyone pirates textbooks anyway). actually shifrin would also be better

>>11864373
Don't know Shifrin, but I agree that do Carmo is not a good starter book. imo the best book to start with is O'Neill's "Semi-Riemannian Geometry", also oop. The best extremely detailed but also not too useful for a begginer books are Lee's "Introduction to Smooth Manifolds" and "Riemannian Geometry".

>Diophantine equations

would rather have all your holes filled with zeros, or ones?

>>11864470
0s
I'm not gay bro

>>11864470
I fill the emptiness inside myself with ones.

>>11864194
based
>>11864170
absolutely embarrassing

[math]A,A[/math]
[math]B,B[/math]
[math]E,E[/math]
[math]Z,Z[/math]
[math]H,H[/math]
[math]I,I[/math]
[math]K,K[/math]
[math]M,M[/math]
[math]N,N[/math]
[math]O,O[/math]
[math]P,P[/math]
[math]T,T[/math]
[math]Y,\Upsilon[/math]

>>11864484
Why is capital upsilon not used? It's beautiful.

>>11864487
[math]\Upsilon,\gamma[/math]

>>11864489
[math]\Gamma[/math]

>>11864484
fellow anime-posters you have to make it and write text books with Kanji- and hiragana- and katakana-named variables

>>11864491
[math]\text T,\Gamma[/math]

>>11864499
>Pic
What am I looking at here?

Can I graph a cubic function with my coom?

>>11864492
That already happens.
https://en.wikipedia.org/wiki/Yoneda_lemma
> The Yoneda embedding is sometimes denoted by よ, the Hiragana kana Yo.

>>11864492
I was thinking about introducing cyrillic letters.

>>11864502
I'm pretty sure that's one of the Araragi sisters, but I can't remember their names.

>>11864502
[math]l,\iota[/math]

>>11864503
[math]\Upsilon(x)=\alpha x^3+\beta x^2 + \gamma;\alpha,\beta,
\gamma \in \mathbb{R}[/math]

>>11864510
yes and also it was originally 圭 for involutive quandles but i would like for it to be more common
>>11864511
cyrillic is too similar to greek and latin

>>11864518
>>11864511
https://en.wikipedia.org/wiki/Tate%E2%80%93Shafarevich_group
it already happens

>>11864518
Best European letters, though.

>>11864519
Nice.

>>11864519
I hate Cyrillic so much, bros.

>>11864159
>The absolute state.
No, it's a good thing. I am one hundred percent willing to not be able to use omicron if it means retards can't either.
>>11864492
I've already learned how to do greek and hebrew letters by hand, that's quite enough, thanks.

[math][\gamma]:\omega \mapsto \int_\gamma \omega[/math]

>>11864523
Mongolian or Tibetan script would be bonkers too

>>11864533
which hebrew letters do you need other than aleph?

I'm trying to prove the inequality involving the sums [math]|\sum_{j=1}^n a_j|^2 + |\sum_{j=1}^n(-1)^j a_j|^2[/math]. I'm having trouble with two aspects of expanding these sums and would appreciate some help.

First, for the first sum, it's easy to show that it is equals to [math] | \sum_{j=1}^n a_j^2 + 2 \sum_{j\neq i} a_ia_j |[/math]. Why do the absolute values drop away in this sum? Doesn't that require showing [math] \sum_{j=1}^na_j^2 \geq 2\sum_{j\neq i} a_ia_j [/math]? This doesn't really seem trivial to me.

Second, I cannot come up with a formula for the second sum. I tried using the multinomial theorem and got to the following sum: [math](\sum_{j=1}^n a_j)^2 = \sum_{j=1}^n a_j^2 + 2\sum_{i,j s.t. i and j have the same parity} a_ia_j -2 \sum_{i,j s.t. i and j don't have the same parity} a_ia_j [/math]. I don't really know where to go from here.

>>11864510
>category trannies forcing anime letters into math
pottery

>>11864545
Beth is also common in set theory.

>>11864545
> which hebrew letters do you need other than aleph?
Not him but gimel (https://en.wikipedia.org/wiki/Gimel_function ℷ) and beth (https://en.wikipedia.org/wiki/Beth_number ℶ).

>>11864552
beth is just a rotated disjoint union symbol
>>11864555
fair enough. thanks for the trips

>>11864547
>why do the absolute values drop?
because [math]|x|^2=|x^2|[/math] and [math]x^2\geq 0[/math] always.

>>11864555
>>11864552
>>11864545
curious that the jewish letters are exclusively used in set theory. this reflects on the nature of set theory as a field
origato

>>11864545
Yeah the Mongol letters would be pretty neat. Thanks for the idea. I am actually denoting stuff using the Futhark runes, but it remains to be seen whether they will get past censorship. Most likely not, I'm afraid.

>>11864547
>>11864564
and actually, [math]\sum_{j=1}^na_j^2 \geq 2\sum_{j\neq i} a_ia_j[/math] *is* trivial by using the aforementioned

>>11864566
kek

>>11864545
I want properly typeset traditional Mongolian in textbooks. Vertical orientation and all. All mathematics should be written sideways.

>>11864567
phd thesis?
>>11864572
yes very much

>>11864574
A potential paper before that, but eventually thesis yes. I also constructed a category I called [math]\Omega\textbf{-SS}[/math] and my supervisor just laughed at it and asked if he should be afraid of me as he is jewish.

>>11864547
[math]\sum_{j=1}^n(-1)^j a_j=\sum_{2j=2}^n(-1)^{2j} a_{2j}-\sum_{2j-1=1}^n a_{2j-1}[/math]. Now I dont know what exaclty youre trying to show, but if youre going to square that sum, then I'd imagine perhaps you could consider it as an expansion of the form [math](x-y)^2[/math]

>>11864547
I dunno what the fuck you're doing at the bottom, but the second sum is just [math]|\sum a_j^2 + 2\sum_{j\not= i}(-1)^{i+j}a_i a_j[/math] . It's the same thing as the first one with a negative sign added.

>>11864576
lmao be careful teichmuller-kun.

Is the Shakarchi series and Jacobson's Basic Algebra 1+3 enough preparation for grad school? Also what are the prerequisites for Langs' Algebra, I heard it was impossibly difficult?

>>11864551
Would you rather we use [math] \lambda [/math] again for the 23rd time?

There was a post with discord link for Munkres study group. Can someone repost it?

>>11864588
Basic Algebra 1+2*

>>11864576

>>11864590
Yes.

>>11864593
No, there wasn't.
At least, if there was, janny deleted it very, very fast.
>>/sci/?task=search&ghost=&search_text=munkres

>>11864588
lang algebra probably would be difficult to read cover to cover. i use it as a review when i feel iffy on some concept

>>11864600
Never mind, found it.
>>/sci/thread/S11797848#p11799975
Now fuck off and don't come back.

>>11864590
lambda sounds funny
say it with me
Lam
Da.

[math]\lambda[/math] is quite literally the greatest symbol of all time

>>11864600
thank you janny for defending the fine users of this general from sissification grooming

>>11864599
Welp, dubs are always good advice

>>11864606
>not lam buh duh
ngmi

>>11864609
for me, its [math]\alpha[/math]. Just so easy to write down

>>11864587
At least I didn't use the S-runes, but I must admit that it does indeed look a bit nazish. I didn't even consider that aspect before he mentioned it. The idea was to have a certain structure on categories and then take the skeletons which would give Skeletal Structure = SS. Accompanying that was a functor and a comment
>We shall call this the \emph{skeletalising functor}, or more briefly \emph{skeletor}
which he thought was a good name. Don't write stuff drunk, friends.

>>11864597
Yes hello based department.

>>11864615
God, every time I write it it's lop-sided I hate it

This thread is very interesting, always run out of symbols. Guess I'll try nordic runes for my next paper just for the sake of extra asspain. Also [math]\partial_i[/math], [math]\partial_{x^i}[/math], or [math]\frac{\partial}{\partial x^i}[/math]?

>>11864614
https://en.m.wiktionary.org/wiki/File:LL-Q150_(fra)-0x010C-lambda.wav

this is how ridiculous you sound

>>11864618
\usepackage{allrunes}

>>11864600
BASED JANNY
>>11864606
Lamb-da

>>11864626
Thanks, but the "asspain" was actually ment for the reader :^)

>>11864618
Any paper with runes in it is going to get shot back from the editor with a message telling you to stop being a fuckhead

how do you write chains of arbitrary length?

Maybe im autistic, but i always feel guilty writing [math]A_1\subset A_2 \subset A_3\subset ...[/math] when the index set might not be countable (even if the end result is some finiteness hypothesis on chains)

>>11864629
Yes but that allows you to use them.

>>11864633
[eqn] \text{Chain}_{n\in I}\left(A_n\right)[/eqn]

Could Mandarin be used for math symbols? You could use them to derive poems.

>>11864618
[math]D_i[/math] for maximum speed, obviously.

>>11864618
>[math]\delta_{x^i}[/math]
stop fucking writing subscripts as exponents you goddamn geometards

>>11864582
Could you explain how you got that? I've been toying with the multinomial theorem for the past two days but couldn't really make sense of it. Also I think your answer is exactly what I have. I just split it up into the cases where i+j is an even number and i+j is odd.

>>11864661
Bro, bro, bro.
Have you tried doing [math]b_j = (-1)^j a_j[/math], using binomial, and then transforming back with [math]a_j = (-1) ^j b_j[/math]? Because if anon's formula is correct that's probably how he got it.

>>11864635
Ah ok thanks again then!
>>11864654
see pic. Also no.

>>11864570
Oh wow I'm actually retarded thanks. I knew [math]\sum_{j=1}^n a_j^2 [/math] was greater than or equal to 0 but I just realized that [math]a_ia_j[/math] could be negative so it shows that the sum of the two terms are greater than or equal to 0.

Post favorite Greek letters.
For me, it's [math\xi][/math].

>>11864674
[math]\xi[/math]

>>11864674
>>11864676
fuck you

>>11864661
I guess it is the multinomial theorem, but it's a bit overkill to appeal to that formally in the case where the exponent is 2, I think.
You're trying to expand [math]((-1)^1a_1+(-1)^2a_2+...(-1)^na_n)((-1)^1a_1+(-1)^2a_2+...(-1)^na_n)[/math] . You expand this out by selecting one element out of each bracket in all possible ways. There's only one way to select a_j twice (and [math](-1)^{j+j} = 1[/math] ), but there are two ways to get [math](-1)^{i+j}a_ia_j[/math] for distinct indices since you can pick them in either order.

>>11864674
[math]\eta[/math]

>>11864676
die

>>11864677
>>11864682
[math]\sum_{\xi_i \zeta_j} \xi_i \zeta_j[/math]

>>11864674
[math]C8\Xi ^o\omega ^o[/math]
Xi and omega allow you to make an octopus and a cat face.

[eqn]\frac{\bar{\Xi}}{\Xi}[/eqn]

>>11864685
>C8Ξ
That's kind of nifty.

>>11864667
I see it now. That's what I did when I first tried it but I just couldn't seem to get it to work out but now it's super obvious. There are two possible types of tuples: (0,..., 2, ... 0) or (0, ..., 1, ..., 1, ...,0). The first one has a 2 in one of the positions and this gets us the squared terms in the sum. The second one has two ones and the rest 0's. Then we get [math](-1)^ia_i * (-1)^ja_j = (-1)^{i+j}a_ia_j[/math] for the tuples of the second type. Thank you everyone.

>>11864681
sqrt(-1)
the symbol for the aceleration due to gravity
the symbol for the aceleration due to gravity
eulers number
the set of the real numbers.

[math]\int_\Xi ^\Lambda \xi^\xi \zeta^\zeta d\Pi[/math]

>>11864689
Thanks.

>>11864678
Idk maybe I'm autistic but I was really bent on using the multinomial theorem.

wish I could be tutored by wildberger and become a rational chromegeometer

[eqn]\Pi_{\eta\in\zeta} \left(\frac{\int_\omega^\xi\sum_{\pi\in\gamma}\rho^\eta_\pi d\alpha}{\lim_{\Gamma\rightarrow\infty}\frac{d^\eta}{d\Omega^\eta}\beta_\Gamma(\Omega)}\right) [/eqn]

>>11864695
What does that mean?

>>11864710
he's having a stroke, somebody call 911

>>11864710
Sorry forgot pic got too excited

>>11864710
Based.

>>11864711
Good question.

Which is best for career prospects frens.
Disregarding the great satan of careers, f*nance
Maths vs Maths w/ statistics vs Maths w/ economics?

>>11864729
Pure maths, win a millennium award, turn it down, then live with your Mom for the rest of your life.

>>11864731
this

>>11864729
Maths with stochastics

>>11864695
[math]\xi ^{ \xi} \zeta ^{\zeta} \int _{\Xi}^{\Lambda} d \Pi = \xi ^{\xi} \zeta ^{\zeta} \Pi ([\Xi , \Lambda])[/math]

>>11864729
Unironically? Applied math, e.g. dynamical systems with specialization neural networks or information geometry.

>>11864763
>information geometry.
What the hell is this?

>>11864768
>Lets take a fuckload of measures and turn it into a manifold LOL.
this

The truth is people should never have to apply their crafts out of need because capit*lism requires you to. If it turns out to have applications good but your life shouldn't depend on it.

>>11864789
That looks expensive.

>>11864588
bump

>>11864814
you don't need to bump the second most active general on the board retard

>>11864821
>second
I personally like to pretend /sfg/ doesn't exist.

>>11864821

only if at least 60% of that traffic was mathematics

>>11864789
i agree with everything except the loli wallhangs

>>11864828
What's wrong with /sfg/?

Tips for studying math as a person with a low frustration tolerance.

>>11864789
based
olds hags will SEETHE at this webm

>>11864850
Don't.

>>11864850
All good things are paid for in blood anon

>>11864841
It's kinda shitty tbqh.
Well, shittier than here.

>>11864853
>using 11 year olds to hold up your graph saying most men aren't attracted to 11 year olds
what did he mean by this

>>11864853
Why the big spike between 10 and 11?

>>11864861
>>11864859
please don't encourage mentally ill pedophiles, thanks

>>11864861
puberty
>>11864865
post wall cope

[math]\forall \alpha \in \mathbb{Z}^+, \alpha ^5=....\alpha[/math]

>>11864861
rigged dataset, probably
the dropoff at the end is way too drastic and too fast to be believable
and even if it was the truth and the study was anonymous, there's no way that 95% of men would admit to wanting to fuck a 12 year old if they suspected she was 12. pedophilia is shameful

>>11864869
Yeah, I'd expect the 20s to be the highest.

why are french mathematicians always so edgy

>>11864882
Name three (3).

>>11861953
convexity, coercivity and lower semicontinuity

>>11864888

Descartes, Galois and Cédric

>>11864897
How was Descartes edgy?

>>11864900

20% of his text have nothing to do with the work at hand but bragging about how it's better than previous developments and the works of his contemporaries

>>11862879
That's an easy one. That was probably an A1 on a putnam.

2018 = 2*1009 or 1*2018 only as well, so this is actually really easy.

in the first case,
1 = 3a - 2018 and
(2018)^2 = 3b-2018 so
a = 2019 / 3 = 673 and
b = 1358114 is one possible answer.

Other one is for
2^2 = 3a - 2018 so a = 674 and
b = 340033.

redpill me

>>11864906
Descartes was the most important philosopher of his time and one of the most important mathematicians. He wasn't wrong.

>>11864915

doesn't make him not an edgelord

>>11864906
>20% of his text have nothing to do with the work at hand but bragging about how it's better than previous developments and the works of his contemporaries
The fact that it's only 20% shows you that he was only partially a philosopher

If [math]v[/math] is the velocity of an object, then what does the quantity [math]v^2[/math] physically represent?

>>11864945
the velocity of an object squared

>>11864949
How does one square an object?

>>11864949
No, like what is the physical interpretation

Like does it mean velocity square area or something? Like the [math]\frac{v}{t}[/math] means acceleration

someone... please... explain divisors...

>>11864956
Bro just take formal sums of irreducible subvarieties. What's even confusing you?

>>11864964
what... is... the... meaning... of... it...

>>11864970
It's one of those things where if you stack large piles of trivialities meaningful results pop out.

>>11864955
>No, like what is the physical interpretation
not everything has a physical interpretation, not everything needs one, and you shouldn't automatically assume, attribute, or visualize a given mathematical quantity to a physical counterpart.

if v is velocity, then v^2 is the velocity squared. It's also the twice the kinetic energy divided by the mass. It's many things.

>>11864988
So it can be thought of as an objects kinetic energy per twice unit mass?

Maybe it means how much energy each unit mass is carrying for the object, but maybe you halve it because its symmetric? idk

>>11864976
>It's one of those things where if you stack large piles of trivialities meaningful results pop out.
name 10

>>11865023
Categorical imperative and ZFC.

>>11864674
φ

>>11864710
Wtf how can you do math with all these letters???? You do math with numbers not letters!!!!! wtf!!!!! Explain pls!?!?!?!?!?!?

>>11864710
wat is this?

>>11864914
is Australia a country?

>>11864882
>>11864888 (Checked)
>>11864897
Grothendieck instead of Descartes. The remaining two stand strong

>>11863921
Some candidates are squid girl, haruhi and steins;gate.

>>11864502
I recognize that thigh. It's Tsukihi Arararagi from monogatari project.

What’s the prep material for understanding probability? I want to learn about things similar to the Monty Hall Door thing. How much, if any, math prep do I actually need for that?

>>11865393
Calculus and a working PFC

Planning on taking a course in Riemannian geometry in September. Currently doing a course in modern differential geometry, so I'll have that under my belt by the end of summer. I have not taken a course in ODEs, however. Should I spend some time during the next two months learning it for Riemannian geometry?

>>11865393
the monty hall thing is not a serious probability problem
i'd suggest you start with some high school olympiad probability problem prep guide, sounds like that's what you're looking for

bros... i love you...

>>11865642
don't do it bro it's not worth it

>>11864618
[math] \partial_i [/math] is best when the meaning is clear. I believe that notation should be minimalistic, so few notations which are flexible but still defined rigorously.

Do you guys know if mathematical proofs can be copyrighted? Let's say somebody publishes a book of exercise, can I just use their solutions without quoting them?

>>11865837
That would come under academic dishonesty

>>11865023
Literally the entirety of algebraic topology.

>>11865852
Yeah but I couldn't be sued right?

>>11864633
What are you asking? Looks to me that von Neumann naturals already fulfill your condition.

[math] A_1 = \{\} [/math]
[math] A_{n+1} = A\cup \{A\} [/math]

>>11864633
What are you asking?
Looks to me that von Neumann naturals already fulfill your condition.
With [math] A_0 [/math] any set, let [math] A_{n+1} = A_n \cup \{A_n \} [/math].

>>11864633
What are you asking?
Looks to me that von Neumann ordinals already fulfill your condition.

With [math] A_0 [/math] any set, let [math] A_{n+1} = A_n \cup \{A_n \} [/math].

>>11865988
>>11865991

thats the point, the index set might not be over the naturals, and labelling the index with 1,2,3 etc implicitly assumes it is natural, when it isnt necessarily

>>11865993
I'm not sure I follow, but in ZF there's uncountably many ordinals, which can be seen as indexing themselves, and two of them either fulfill either [math] \alpha \subset \beta [/math] or [math] \beta \subset \alpha [/math].
Looks like you need power set and replacement for that.

>>11864633
[math]A_i \subset A_j [/math] for all [math]i < j[/math], where [math]i, j[/math] are in some indexing set.

>>11865993
I think I misunderstood your (or this guys) question, nevermind my comment.

can you stop replying to me holy fuck

>>11864734
Stop posting your wife.

Bros....

We moved to this idea that we have a single dominant encyclopedia that was supposed to be the truth for the global AI or something like that. But there’s something deeply pernicious about that. So we’re saying anybody can write for Wikipedia, so it’s, like, purely democratic and it’s this wonderful open thing, and yet the bizarreness is that that open democratic process is on the surface of something that struck me as being Maoist, which is that there’s this one point of view that’s then gonna be the official one.

And then I also noticed that that process of people being put into a global system in which they’re supposed to work together toward some sort of dominating megabrain that’s the one truth didn’t seem to bring out the best in people, that people turned aggressive and mean-spirited when they interacted in that context. I had worked on some content for Britannica years and years ago, and I never experienced the kind of just petty meanness that’s just commonplace in everything about the internet. Among many other places, on Wikipedia.

what happened with this thread?

>>11866779
Yes.

>>11864882
>>11864888
I'm shocked you left out Pascal, dude was The edgy french mathematician

>>11865393
>>11865462
> some high school olympiad probability problem prep guide
Post examples, now I'm curious.

>>11861976
This fact really fucked with me when I first heard it. It didn't help that Weibel uses a bit of odd terminology - epimorphisms are defined to be surjective morphisms, and then he goes on to say that epimorphisms in the usual sense are "morphisms which are epi."

How do I cope with never actually being able to be competent at maths, bros?

>>11867069
In the categories (or at least most of them) he is doing stuff in, they are the same. I see it as a thing that is analogous to the fact that the group of quaternions is not abelian itself but any of its proper subgroups is. In this case you restrict the category of topological spaces to a proper subcategory and get something extra like non-surjective epis. Do I remember correctly that Weibel actually has epimorphisms and epis as two separate concepts but then proves that they are actually equivalent? I have this vague memory, but I really can't remember if it was him and how the definitions were. Probably like if e is an epi and fe = 0, then f=0, or something like that. It's been ages since I read his book. I did it touch it last year, though, as my office mate had it in a pile over my books!

>>11867103
Cheap wine from Lidl, several times a week.

>>11867103
Read philosophy.

nouveau
>>11867252

>>11867046
https://web.evanchen.cc/handouts/ProbabilisticMethod/ProbabilisticMethod.pdf
Here's a good one but it would be difficult for a total beginner

>>11867256
Merci