V.I. Arnol'd's Mathematical Trivium

[ZetaOfThree]

Check out this collection of mathematics problems, published in 1991, by V.I. Arnol'd called "A Mathematical Trivium". Here's the link:
http://www.math.upenn.edu/Arnold/Arnold-Trivium-1991.pdf
Apparently, these problems are meant to be solvable by the end of your undergraduate (math) education. Arnol'd says "A student who takes much more than five minutes to calculate the mean of $\sin^{100}{x}$ with 10% accuracy has no mastery of mathematics, even if he has studied non-standard analysis, universal algebra, supermanifolds, or embedding theorems." I'd be interested to hear what everyone thinks about the problems. Personally, I found many of them to be quite difficult. What do you think?

 

[Orodruin]

Arnol'd says "A student who takes much more than five minutes to calculate the mean of $\sin^{100}{x}$ with 10% accuracy has no mastery of mathematics, even if he has studied non-standard analysis, universal algebra, supermanifolds, or embedding theorems." I'd be interested to hear what everyone thinks about the problems. Personally, I found many of them to be quite difficult. What do you think?

Didn't look into it more than the sin^100 problem but that was pretty fun. First estimate was 6% off, got it down to 3‰ upon using a different method. Do I get bonus points for literally having done it on the back of an envelope? :p

 

[ZetaOfThree]

Nice! You should try some of the problems in Trivium. There some similar themed problems.