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/math/ - Mathematics

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25 Dec 2021Mathchan is launched into public
Catalog Archive

File: 3-adic integers with dual colorings.png ( 660.99 KB , 1200x1200 , 1641009124540.png )

Image
  No. 94
Reply
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.
>>
  No. 98

File: tikz-cd-doc.pdf ( 264.95 KB , 1641011017028.pdf )

Image
Mathchan supports embedding commutative diagrams:
A→aBb↓↑cC=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.

File: images.jpeg ( 23 KB , 554x554 , 1713434320788.jpeg )

Image
  No. 714
Reply
>>721
6 posts and 5 image replies omitted. Click here to view.
>>
  No. 722 >>723
>>721
Why don't you like combinatorics?
>>
  No. 723
>>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
>>
  No. 776 >>777
Was posed to me recently:

Do there exist nxn matrices X, Y such that XY - YX = I_n? Provide an example or proof of the negative.
>>
  No. 777 >>778
>>776
Yep, it exists. For
X=A⋅B X=A \cdot B
with A,B
n⋅n n \cdot n
matrices
≠In \neq I_n

because the product between matrices isn't commutative.
So \( X \cdot Y-Y \cdot X = A \cdot B \cdot Y - Y \cdot A \cdot B = I_n)
>>
  No. 778
>>777
Edit: Yep, it exists. For
X=A⋅B X=A \cdot B
with A,B nxn matrices
≠In \neq I_n

because the product between matrices isn't commutative.
So
X⋅Y−Y⋅X=A⋅B⋅Y−Y⋅A⋅B=In X \cdot Y - Y \cdot X = A \cdot B \cdot Y- Y \cdot A \cdot B = I_n

File: math_curriculum.png ( 1.12 MB , 1140x4777 , 1713088252224.png )

Image
  No. 688
Reply
>>689 >>694 >>756
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.
7 posts omitted. Click here to view.
>>
  No. 756
>>688
Why haven't anyone named the books yet. Just fucking read the titles. I need the names of last two books
>>
  No. 757
>>
  No. 758 >>768

File: 8.jpg ( 6.91 KB , 257x400 , 1714159727670.jpg )

Image
Last book is Topics in Transcendental Algebraic Geometry by Phillip A. Griffiths and other one is Geometric Invariant Theory by Mumford.
>>
  No. 768
>>758
Thanks Anon.
Its /thread/
>>
  No. 775
The early curriculum is great for building a solid foundation. But it seems very single-minded on getting to abstract results in algebraic geometry. You can easily miss the trees for the forest by doing that.

>Are the books shown in the picrel enough to cover the mentioned topics.
They mostly seem to be selected for being the "hardest" book on the particular subject, which is not always the best. For instance BottTu is definitely not the hardest for anything it covers, but the clarity of exposition makes it a worthwhile read.
>how long would it take
Depends how much time you devote to it. If you spend 40-50 hours a week on studying, and you study efficiently, you could maybe finish this in five years. How much you would retain with no interaction from a mathematical community is uncertain, probably low. It takes years of being immersed in the field for knowledge to really sink in.

File: 3t0kod.jpg ( 76.97 KB , 800x450 , 1675025207218.jpg )

Image
  No. 346
Reply
>>347 >>385 >>380 >>429 >>507 >>525 >>530 >>544 >>659
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
36 posts and 3 image replies omitted. Click here to view.
>>
  No. 745 >>746 >>771
>>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.
>>
  No. 746 >>747
>>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?
>>
  No. 747
>>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
>>
  No. 771 >>774
>>745
All I can say is extensively study the solutions and work out all the tricks you can find. Think long about how you could've come up with that yourself and then burn that into your mind
>>
  No. 774
>>771
>Think long about how you could've come up with that yourself
but I never find an answer to that. It's always like,"Oh, if I had thought of this one random trick/manipulation, I would've done the problem."

I'm never able to figure out how to think of those lil tricks without seeing the solution. This goes for all types of math, not just captcha problems.

please help me

File: xiom.png ( 380.54 KB , 1080x980 , 1663002740804.png )

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  No. 299
Reply
>>604 >>709 >>711 >>732 >>767
When did you realize that the reals are fake?
Mathematics can do without infinities.
14 posts and 1 image reply omitted. Click here to view.
>>
  No. 760
>>759
The problem is that one would need to restrict to eventually zero sequences, the sequence you'd construct however wouldn't be eventually zero.
>>
  No. 761
>>712
Your post made me realize that being able to conceptualize abstractions that don't actually exist is what we learn to do as toddlers; finitists are essentially just stuck on the adult version of this leap. That's pretty funny.
>>
  No. 763
>>604
Hello
>>
  No. 767
>>299
ggggggggggg
>>
  No. 773
Полностью стильные новости индустрии.
Важные эвенты мировых подуимов.
Модные дома, бренды, гедонизм.
Новое место для модных хайпбистов.
https://breakmoda.ru/

File: 1712331276459113.png ( 124.7 KB , 300x263 , 1715114011855.png )

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  No. 769
Reply
https://arxiv.org/abs/2405.03599

https://www.youtube.com/watch?v=1emC3ncjblU

https://people.mpim-bonn.mpg.de/gaitsgde/GLC/

File: asdasdas.png ( 2.99 KB , 605x152 , 1697767208017.png )

Image
  No. 512
Reply
>>532 >>535 >>539 >>548 >>713 >>744
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.
>>
  No. 555
>> 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.
>>
  No. 706
>> 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
>>
  No. 713

File: k-on.jpg ( 28.3 KB , 466x545 , 1713302881989.jpg )

Image
>>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
>>
  No. 744
>>512
I'm a retarded dumb zoomer and I solved it so.... yeah my iq is like 120+ or sumn
>>
  No. 755
iq autism

File: 1705233653759.png ( 201.38 KB , 1139x804 , 1713480390587.png )

Image
  No. 724
Reply
>>727 >>731
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.
>>
  No. 741 >>742
>>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?
>>
  No. 742 >>743
>>741
oh i forgot you had to be on the phone lol, fair enough
>>
  No. 743
>>742
I think I'll buy wolframalpha, it has dynamic pricing for shithole countries and considers PPP unlike chatgpt that charges dollars for everyone.
>>
  No. 751 >>754
Sorry if I'm late, the captcha is hard. If you go looking, you will find free wolfram alpha for android.
>>
  No. 754
>>751
No problem mate. Couldn't find anything that works on rutracker. Where exactly must I be looking?

File: 1642980098311.gif ( 3.73 MB , 406x640 , 1713832706815.gif )

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  No. 749
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Im new.
>>
  No. 750
Hello

File: 8-41-08.png ( 285.09 KB , 2220x892 , 1713077717968.png )

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  No. 685
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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.
>>
  No. 720
The answer is [math]2017 \cdot 2018[/math]
>>
  No. 725 >>726 >>735
I deeply regret showing my normalfag friends this site... forgive me mathchanners.
>>
  No. 726 >>733
>>725
Why?
>>
  No. 733
>>726
This board is being flooded with useless discussion
>>
  No. 735
>>725
it's okay, all these posts will be drafted to /ret/ - retards soon

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