Math Puzzles Thread

>>8443744
why am i so alone

>>8443744
Let [math] F: \comp^2\to \comp^2[/math] be given by F(x,y)=(p(x,y), q(x,y)) where p and q are polynomials. Assume that the Jacobian determinant [math] p_xq_y-p_yq_x[/math] is a non-zero constant.

Show that the components of [math] F^{-1} [/math] are polynomials.

(This was a fun extra credit problem in my complex analysis class).

>>8443750
OP was asking for hard problems, not trivial bs like this

>>8443750
>doesn't say which field his polynomials are defined over
>his shitty school assigned this basic homework problem in complex analysis and not even in vector calc
what sad excuse of a university do you go to? i want to know so i can avoid it forever

File: labyrinth.jpg (55KB, 768x433px) Image search: [Google]

55KB, 768x433px

>>8443744
You're in a room with two computers and two doors. One computer always tells the truth one always lies, you dont know which. One door leads to life and the other to death, you dont know which. What one question can you ask verbatim to both computers that will show you which door to pick?

>>8443771
if i had a program on a turing machine that told me which door lead to life, would the program terminate?

>>8443771

Does the 1st door lead to death and is the other computer lying?

>>8443771
Which way would the other computer tell me to go? Both point to death

>>8443790
the answer to "is the other computer lying" is always yes, so that's not helpful, and the first part of your question doesn't help on it's own

>>8443744
That's a pleb level problem, loser

>>8443771
>>8443771
"What would the other computer say is behind the door directly in front of me?"

This way, the answer you receive is guaranteed to be false.

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>>8443809
Solve it then, fag.

>>8443803
This. It's a simple riddle.

Fuck sake this was in Yu-Gi-Oh lmao

>>8444038
kek

>>8443771
>>8443803
But isn't it unnecessary to have two computers if both give you the same answer? Couldn't this riddle be done with only one computer?

>>8444033
>solution is left as a exercise for the reader

>>8443744
Using only chords, divide a circle into equal area pieces with no two pieces congruent.

>>8443766
>which field
Complex numbers obviously

Why don't you post your solution, friend? :^)

>>8445010
the exercise requires only plugging through the definitions, do your own homework, there's /sqt/ threads for these kinds of things

>>8445061
I know how to do it. Like I said, it was an extra credit problem. Why don't you try to work it out; it's not as trivial as you think.

>>8443744
http://www.claymath.org/millennium-problems

>>8443744
hardest problem:
prevent our doom

>>8445103
i did that in my second year during vector calc like i already said

>>8445134
Well then it shouldn't be any trouble for you to post your solution, or at least an outline. Or you can just keep repeating how easy it is, and never put your money where your mouth is :^)

>>8445139
its literally not worth my time, i'm sure you can find dozens of answers on stackexchange

>>8443750
this was posted a couple times a couple of weeks ago. I never saw a solution. I thought this was a hard problem.

https://en.wikipedia.org/wiki/Jacobian_conjecture

is the n=2 case easy?

>>8445162
https://en.wikipedia.org/wiki/Jacobian_conjecture

OK if you say so Mr Big Man :)