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/math/ - Mathematics


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25 Dec 2021Mathchan is launched into public


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This board is for the discussion of mathematics.



Equations can be embedded in multiple ways:
  • \eqn{...}
    or
    \math{...}
    command substitutions
  • \[ ... \]
    or
    \( ... \)
    block substitutions
  • $$ ... $$
    or
    $ ... $
    special block substitutions
  • \begin{equation} ... \end{equation}
    or
    \begin{math} ... \end{math}
    environments
  • by starting a line with
    ,,
    or
    ,eqn
    like one commonly would with >greentext.


Matrices can be embedded by using
\begin{matrix} ... \end{matrix}
or
\begin{array} ... \end{array}
environments in any of the above ways to embed equations, or by starting a line with
,mat
,
,pmat
,
,smat
,bmat
,
,Bmat
,
,vmat
or
,Vmat
and using
&
and
\\
symbols to delineate between columns and rows respectively.

Arrays can be embedded by using
\begin{array}{c|c:c} ... \end{array}
environment in any of the above ways to embed equations, or by starting a line with
,arr{c|c:c}
Post too long. Click here to view the full text.
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Mathchan supports embedding commutative diagrams:
AaBbcC=D \qquad\begin{CD} A @>a>> B \\ @VbVV @AAcA \\ C @= D \end{CD}

This can be done by using the
\begin{CD} ... \end{CD}
environment in any of the above ways to to embed equations, or by specifying your code after starting a line with
,cd
.

If KaTeX's support is insufficient, diagrams can rendered using the
\tikzcd{...}
command or by using the
\begin{tikzcd} ... \end{tikzcd}
environment.
For example, pasting the following excerpt from the attached PDF (TikZ-CD manual):

\begin{tikzcd}[row sep=scriptsize, column sep=scriptsize]
   & f^* E_V \arrow[dl] \arrow[rr] \arrow[dd] & & E_V \arrow[dl] \arrow[dd] \\
   f^* E \arrow[rr, crossing over] \arrow[dd] & & E \\
   & U \arrow[dl] \arrow[rr] & & V \arrow[dl] \\
   M \arrow[rr] & & N \arrow[from=uu, crossing over]\\
\end{tikzcd}

Will render as the following figure on Mathchan:



The drawback is that you will have to pause typing and wait until the diagram renders while KaTeX can be displayed instantaneously.
It is recommended that you compile any LaTeX code yourself - or in Overleaf - before attempting to paste it on Mathchan.


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Please name all the books in picrel. Also review the curriculum shown. Are the books shown in the picrel enough to cover the mentioned topics. If so how long would it take.
3 posts omitted. Click here to view.
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>>688
aim high, it doesn't just have to be a dumb desk engineering job either.
the effort doesn't just stop at reading hard books, if you just go for a programming job you're being lazy, and that's not why we're here on mathchan
it's not 'follow this hobby math curriculum and do a bunch of toy analysis proofs'
which is why our list doesn't look like a typical math or CS major, because it is not courses for courses' sake
it doesn't stop there, it continues in your work - if you know theoretical physics and a base of mathematics, you could be doing literally anything
it would be lazy and shameful to stop there
you should be working on something big and important, gather experience in a different field, transform it with mathematics, start your own company
anything less is a waste
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>>694
I aim trying to aim high anon. This curriculumn looked difficult. So should I start with sheafification?
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>>695
Almost all the recommendations there are great. It recommends first getting proficient at single- and multivariable calculus before moving onto analysis but I prefer books that treat both simultaneously, like Amann and Escher's three-book analysis series.
>>
>>689
Even Urs Schreiber approves of the /mg/ curriculum:
https://nforum.ncatlab.org/discussion/15070/anisomorphism/?Focus=102597#Comment_102597
>>
>>688
Why haven't anyone named the books yet. Just fucking read the titles. I need the names of last two books


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What I said in the subject. It's so easy to prove. Search the problem and solve it, simple as that.
5 posts and 1 image reply omitted. Click here to view.
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>> 548
It's obviously not a real proof. It's written in MS Word (probably) by someone with elementary knowledge on number theory. It contains so many mistakes, I don't even want to read it.
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>> 555
Lmfao proof to the contrary by
>wrong formatting software
and
>inadequate credentials of the author

at least referring to the mistakes would be worth something, the other two points have zero relevance to how true any of the statements are
>>

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>>512
This is a very safe statement to make when you don't use "iff", I'd be willing to wager it's true and factpilled
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>>512
I'm a retarded dumb zoomer and I solved it so.... yeah my iq is like 120+ or sumn
>>
iq autism


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If you had a math exam and you could use your phone with internet while attempting the paper, what service would you use to solve questions?
Topics:
-Propositional Calculus
-Methods of Proof
-Boolean Algebra and Circuits
-Sets, Relations and Functions
-Combinatorics
-Some more Counting Principles
-Partitions and Distributions
11 posts and 1 image reply omitted. Click here to view.
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>>740
That doesn't work on android. You want me to install in on a PC and remote control it via my phone while attempting the exam?
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>>741
oh i forgot you had to be on the phone lol, fair enough
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>>742
I think I'll buy wolframalpha, it has dynamic pricing for shithole countries and considers PPP unlike chatgpt that charges dollars for everyone.
>>
Sorry if I'm late, the captcha is hard. If you go looking, you will find free wolfram alpha for android.
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>>751
No problem mate. Couldn't find anything that works on rutracker. Where exactly must I be looking?


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When did you realize that the reals are fake?
Mathematics can do without infinities.
8 posts omitted. Click here to view.
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>>299
Sorry, I haven't seen that notation for the last equation before, is that supposed to be axiom of infinity? Does y' represent successor? I've seen {y} U y and S(y).
>>
>>709
it is, that notation is definitely nonstandard. Similar notation is y^+
>>
>>710
Thanks
>>299
I mean, if ZFC still works without it, there could be an argument that it isn't 'real'. Could remove Infinity, Replacement, Choice, and I think Foundation.
>>

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>>543
Bizarre shit because while infinities aren't tangibly real, finite integers also aren't.
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>>299
I have never understood diagonalisation argument.


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Im new.
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Hello


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So, I have a cousin who wants to win medals in math competitions, especially IMO. Post resources, guides and tips for olympiads.
his prep level: he's 12yo(7th standard), has completed mathematics books upto the 10th standard level. What should be his target next? And how do I help him clear doubts? We don't have decent teachers where we live, and the internet doesn't help much
34 posts and 3 image replies omitted. Click here to view.
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>>596
wait shoot youre right bruh

https://www.amazon.com/Topics-Functional-Equations-Third-Xyz/dp/099934286X

you could buy it but idk if its worth it 🥴
>>
>>346
leap day bump
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>>381
Thanks for these books man. I have a question about the last line. When I was 15 years old and very interested in olympiad mathematics, I got greeted by titu andreescu's 104 problems in algebra, and that book alone forced me to never chase the path of math olympiads again. I'm 19 now graduating highschool and I want to study mathematics at university, so i'm getting back into this stuff, but even then, I just visited the book again and I can't solve/understand/crack through a SINGLE FUCKING PROBLEM. The solutions ARE EVEN MORE COMPLEX THAN THE PROBLEMS THEMSELVES.

Also fyi I've never won a mathematical olympiad in my country, I participated for the second time last year and only got through the selection round by cheating, failed in the 2nd round because duh.
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>>745
this is also me and seeing that this is the most active thread on this board, I wanna ask you guys what's the source of the mathchan captcha problems? Also what level of math do you OP's know to be able to solve that shit? Most of it just got over my head wtf. Is it like undergrad/grad level maths or olympiad type?
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>>746
>what's the source of the mathchan captcha problems
Some people who know the lukyon make it and lukyon adds them

>Also what level of math do you OP's know to be able to solve that shit
NGL what i did was solve one easy captcha, memorize the answer, and whenever I need to solve another captcha just refresh until i get back to the one i solved


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I know absolutely nothing about math, my knowledge is basically stuck to 7th grade stuff at best.
That said, even I can tell those wrong captcha answers are nonsensical, to the point I can easily get around verification by simply guessing the right answer.

Just a heads-up
2 posts omitted. Click here to view.
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The answer is [math]2017 \cdot 2018[/math]
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I deeply regret showing my normalfag friends this site... forgive me mathchanners.
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>>725
Why?
>>
>>726
This board is being flooded with useless discussion
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>>725
it's okay, all these posts will be drafted to /ret/ - retards soon


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>>714
pls less combinatorics problems thank you
>>
>>721
Why don't you like combinatorics?
>>
>>722
a math problem general should have some variety but besides that, combinatorics isn't a useful thing to study directly and its problems are ultimately better understood and solved in representation theory frameworks.
when you understand a problem well you are able to turn it into some kind of elementary computations/combinatorics, but this isn't an indication to study combinatorics specifically, than to study mathematics which is inherently meaningful and learn how to convert the abstract formulation

combinatorics really is a subset of other more important stuff, you get combinatorial tools in algebraic topology, number theory, algebraic geometry, homotopy. e.g. simplicial sets contain a lot of what you would ever do with graphs. in number theory you have trees coming from finite fields. in algebraic geometry you have combinatorics of the grasmannian, riemann surfaces, combinatorial ideals, matroids.
just learn other stuff, plain combinatorics is a fad driven by funding for "applied math" and computer science departments. serious combinatorialists (June Huh for example) end up studying homological algebra anyway


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Mathematically speaking, what is the optimal strategy for yahtzee?
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>>499

We'll be playing yahtzee in vrchat this weekend.
  1. Free
  2. Linux-compatible
  3. No GPU required

People are smart
\cap
nice
\cap
cool. 33F6YsgTX8
>>

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Depends if the result is determined as a binary (or trinary) win/loss (+draw?) or if you're playing so that every point difference is $1 or something. Way easier to calculate if it's by point difference because then there's just a single, objective EV calculation and you don't even take the opponent's strategy into account, it can't change the EV of your own move.

If playing for a win and ignoring whether it's by 1 or 100 points, you get into obscene amounts of game theory, future game simulation and even psychological exploitation of mistakes (pointless to play if you're both optimal computers, so the mistakes will be there), and the game tree fucking explodes in complexity