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/math/ - Mathematics

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25 Dec 2021Mathchan is launched into public
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File: 10FA814D-3F99-493D-B028-3E94484555B6.png ( 225.41 KB , 712x2584 , 1640980402330.png )

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  No. 91
Reply
>>185 >>701 >>889
You can solve this, right?
3 posts and 2 image replies omitted. Click here to view.
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  No. 185
>>91
Yes. What's the time limit?
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  No. 700 >>703
Where is this an Enterance Exam to? I do not think I could do it. My undergraduate univeristy is all multiple choice and so I am nearly finished it having barely written a proof. It's awful.
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  No. 701
>>91
sneed
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  No. 703
>>700
I somewhat doubt it is an actual entrance exam. It reminds me of 1st year graduate course of mathematical methods in theoretical physics given that it has a bunch of maths without too much coherence.

Also, I think the ban on electronic calculators is quite futile here.
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  No. 889
>>91
the ideas here are easy but i don't know what C-convergence means
can someone link a book on the topic?

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  No. 878
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>>883
This is a thread to post a paper or book you are reading currently.
>>
  No. 879 >>884
i just started reading complex analysis of Stein & Shakarchi a few days ago. Currently on Cauchy's integral formula
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  No. 883

File: Elliptic Curves Lecture 5 - Isogeny.pdf ( 244.43 KB , 1721355587644.pdf )

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>>878
Right now I'm reading this series on Elliptic Curves. At the last lecture it gives an intelligible argument for Wiles' 5-3 trick.
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  No. 884 >>888
>>879
I like the way this is written. I may read this in the future since I haven't ever completed a book on Complex Analysis.
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  No. 888
>>884
Me too, i think its great at explaining things (although its stuff that i already know in the first chapters). I am a self studying 9th grader and ive also completed its Fourier analysis. I really love the way it teaches

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  No. 780
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>>782
do you look like a scientist?
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  No. 782 >>783
>>780
kill yourself 4cuck bhangi
>>
  No. 783
>>782
Man of cultutre right here
OP should live stream roping himself. Sage goes on all fields
>>
  No. 802 >>885
scientists look like that?
>>
  No. 885
>>802
only monkeys do but oh well
https://www.youtube.com/watch?v=6C-kBVggFrs

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  No. 559
Reply
>>669 >>675 >>607 >>629 >>843
https://newsen.pku.edu.cn/PKUmedia/11888.html

>Of these 24 questions, Wei Dongyi completed 23 and a half, a record that even his coach was amazed by. He often solved all the questions in the first hour of the test. Many of the methods he used were self-invented and were much more concise than the standard processes, and became known as the "Wei Method".

>
In this competition, Wei beat the legendary Tao Zhexuan, who taught himself calculus at the age of seven and won the IMO gold medal at the age of 12, by a time ratio of 1:7. Tao Zhexuan was invited to solve the sixth problem of the finale, which took him seven hours, while Wei Dongyi took only one hour in the competition.

Is it really impossible to be like him with just learning and studying more? Is it really over, is only option actually suicide? Please be brutally honest, I don't want any false hope.(Even though I know the answer)
19 posts and 2 image replies omitted. Click here to view.
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  No. 675
>>559
its experience, solve more problems & learn more methods & you'll get better.
even if you don't its not the end of the world. you can still fuck women without being a three time IMO winner.
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  No. 805

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>>608
Based low-iq proover ideology.
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  No. 817
>>630
Please specify what you have achieved
>>
  No. 843 >>844
>>559
test
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  No. 844
>>843
you realise you dont actually need to post to fill in the captchas right?

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  No. 236
Reply
>>237 >>239 >>242 >>247 >>837
-1/12

contradiction or too complex for mere mortals to understand?
8 posts and 1 image reply omitted. Click here to view.
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  No. 304

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This physicist's treatment of the -1/12 issue from Zee's QFT book is the best treatment of the question I've seen.
>Appallingly, in an apparent attempt to make the subject appear even more mysterious than it is, some treatments simply assert that the sum is by some mathematical sleight-of-hand equal to -1/12. Even though it would have allowed us to wormhole from (1) to (3) instantly, this assertion is manifestly absurd. What we did here, however, makes physical sense.
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  No. 305
Behold, the Barnett-Tooker-Wildberger conjecture.

Let

ζ^b(s)=∑k=1∞^−bn−s\qquad \hat\zeta_b(s) = \sum_{k=1}^{\hat\infty - b} n^{-s}


then

ζ^e+π+2(−1)=eiπ11+0.999…\qquad \hat\zeta_{e + \pi + \sqrt 2}(-1) = \frac{e^{i\pi}}{11 + 0.999\dots}
>>
  No. 315
I still don't get it.
>>
  No. 811
Contraddiction, because in Ramanujan's proof there are mistakes i.e. the term equals zero changes the number of step in the serie and also it's true that
2>Σn=0+∞12n 2 > \Sigma_{n=0}^{+\infty} \frac{1}{2}^n
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  No. 837
>>236
it diverges up, right?
and the limit is the first value something dosent reach
therefore, the limit of the series must be down

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  No. 499
Reply
>>500 >>836
Mathematically speaking, what is the optimal strategy for yahtzee?
>>
  No. 500

File: yahtzee-chaos-2.png ( 2.08 MB , 1920x1080 , 1694701115191.png )

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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
>>
  No. 707 >>836

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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
>>
  No. 836
>>499
have fun?

money is a system of favors, and is as of such an inferior substitution to communal trust and direct manipulation, so even if you are betting like >>707 would imply, focussing on the people in the room is optimal

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  No. 769
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>>825 >>826
https://arxiv.org/abs/2405.03599

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

https://people.mpim-bonn.mpg.de/gaitsgde/GLC/
>>
  No. 825
>>769
probably the most important proof this century
>>
  No. 826

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>>769
Can you describe what are its implications

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  No. 813
Reply
The discrete logarithm
ax=b a^x=b
mod p is polynomial with a,p prime ≠ 2; the question is if a=2 or a is a dialed number is still polynomial? I troved a way, but is a class of solutions.

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  No. 714
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>>721
6 posts and 5 image replies omitted. Click here to view.
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  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
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  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

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  No. 257
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>>258 >>452 >>335
no eureka for today, gentlemen
11 posts omitted. Click here to view.
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  No. 648 >>649
>>641
Because I love reinventing the wheel
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  No. 649 >>650
>>648
Emoji Image you are started from solution when you wrote
x=sqrt[3]p+q+sqrt[3]p−q x=sqrt[3]{p+q}+sqrt[3]{p-q}

If you reinvente the wheel how do you solve
x5+px2+qx+t=0 x^5+px^2+qx+t=0
or
x6+ax3+bx2+cx+d=0 x^6+ax^3+bx^2+cx+d=0
? Emoji Image
>>
  No. 650 >>651
>>649
Me again, edit: when you wrote
x=p+q3+p−q3 x=\sqrt[3]{p+q}+\sqrt[3]{p-q}
sorry for the mistakes Emoji Image
>>
  No. 651
>>650
I said that I guessed it. I kinda remembered the outlook of the original solution with the sum of two cubic roots, but I didn't remember what was inside.
>>
  No. 702
AAAAAAAAA

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