V.I. Arnol'd's Mathematical Trivium

  • Thread starter Thread starter ZetaOfThree
  • Start date Start date
  • Tags Tags
    Mathematical
AI Thread Summary
V.I. Arnol'd's "A Mathematical Trivium," published in 1991, presents a collection of mathematics problems intended to be solvable by undergraduate students. Arnol'd emphasizes that mastery of mathematics should allow students to quickly calculate the mean of functions like sin^100 with reasonable accuracy. Participants in the discussion express varying levels of difficulty with the problems, with some finding them challenging yet enjoyable. One contributor successfully estimated the mean of sin^100 with increasing accuracy, showcasing the problem's engaging nature. Overall, the collection is seen as a valuable resource for testing mathematical skills.
ZetaOfThree
Gold Member
Messages
109
Reaction score
23
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?
 
Last edited by a moderator:
Mathematics news on Phys.org
ZetaOfThree said:
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
 
Nice! You should try some of the problems in Trivium. There some similar themed problems.
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...

Similar threads

Back
Top