558 reputation
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bio website github.com/sw1sh
location Moscow, Russia
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visits member for 1 year, 6 months
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You Should Do The Matasano Crypto Challenges. I did and they are awesome.


Nov
7
comment What are some examples of notation that really improved mathematics?
@NateEldredge I think it is an improvement. Compare vector expressed as a series in usual notation $\sum \langle x,\phi \rangle \phi$ and in bra-ket notation $\sum \langle \phi | x \rangle |\phi\rangle$. The bra-ket notation also can be read not just as sum of vectors with coefficients but also as matrix-vector multiplication just by swapping things around. Also we can treat $\sum |\phi\rangle\langle\phi |$ as an identity and it gives rise to a bunch of useful algebraic manipulations.
Nov
7
comment What are some examples of notation that really improved mathematics?
Einstein's notation is indeed the power of math at its finest! I would add Kronecker and Levi-Civita symbols to this answer.
Nov
7
comment How to put 9 pigs into 4 pens so that there are an odd number of pigs in each pen?
@kriss Thx, next to last was wrong indeed (also the second one), counting to five is hard! Fixed it and also colored the pens for more clearity.
Nov
2
comment When written in decimal notation, every square number has at most 1000 digits that are not 0 or 1. True or false?
[silly]$2^2 = 3.9999999...$ have clearly more than 1000 nines, so it's false[/silly]
Oct
27
comment Counting backwards from $\infty$ and negative cardinality
Who said about any problem? Isn't it just cool?
Oct
27
comment Counting backwards from $\infty$ and negative cardinality
@AsafKaragila I don't understand if there is a correspondence why I can't say they are the same? If size of a set don't behave like a number, I just invent a new type of number and make up an algebra for it to behave it like I want.
Oct
27
comment Counting backwards from $\infty$ and negative cardinality
@AsafKaragila You can call it whatever you want. I just concerned about the meaning of these objects.
Oct
27
comment Counting backwards from $\infty$ and negative cardinality
@AsafKaragila Because it's negative cardinalities.
Oct
27
comment Counting backwards from $\infty$ and negative cardinality
@EuYu It still behaves like infinity in the sum.
Oct
27
comment Counting backwards from $\infty$ and negative cardinality
@AsafKaragila I'm not necessarily talk about the cardinal numbers. I'm not too familiar with them, but this seems like completely different infinity. I have $\#(\infty-1)=-1$ and not $\#(\infty-1)=\aleph_0$.
Jan
11
comment Minimum number of steps needed to solve a rubik cube
It's not the one I'm looking for. This solution I can easily find everywhere, it's more than just 3 steps.
Jan
9
comment Minimum number of steps needed to solve a rubik cube
@RossMillikan I did solve it with those moves many times, it required some thought to it and I liked it :).
Jan
7
comment Minimum number of steps needed to solve a rubik cube
@RahulNarain Probably... If someone will write these moves down it would be great.
Jan
5
comment As shown in the figure: Prove that $X=30.$
@amWhy Nah, I'm done here. I was just a bit bored.
Dec
25
comment Why is 'abuse of notation' tolerated?
Oh I remember how as a freshman I was taking notes on math related lectures and was trying to purify math so that I have no words at all there except titles, names and some minor comments and it should be as compact as possible. Now I can make a 10 page theorem proof in to one page so that I can see a full picture just with one glance, it helps a lot.
Dec
15
comment Change of variables in Belousov-Zhabotinsky reaction
Well, that's what you do when you nondimensionalize your equations. It's a chemistry, so $x,y,z$ are some concentrations so as $A,B$. Then to nondimensionalize a variable $z$ you replace it with something like $\frac{z}{B}$.
Dec
15
comment Change of variables in Belousov-Zhabotinsky reaction
Or $z -> \frac{z}{B}$, $t -> \frac{\tau}{B k_5}$, $x -> \frac{k_5 x}{2 k_3 A }$
Dec
15
comment Change of variables in Belousov-Zhabotinsky reaction
Well just from looking on the 3rd equation I can say, that $z$ was changed to $\frac{z}{k_5 B}$, $t$ to $\frac{\tau}{B k_5}$ and $x$ to $\frac{x}{2 A k_3}$. The rest is easy to do.
Dec
15
comment Change of variables in Belousov-Zhabotinsky reaction
It can be used for further simplification of the system , to get rid if some equations. But I just realized that it's not the question. Do you just need to know what replacements were used?
Dec
15
comment Change of variables in Belousov-Zhabotinsky reaction
Take a look at Tikhonov's theorem