- #1
jackmell
- 1,806
- 54
Hi,
Notice since micromass left, the math challenge sub-forum was removed. Would it be productive to start it again? I just ran into another problem today I felt was a challenge: derive a symbolic (and convergent) expression for \mathcal{L}\left\{\tan(t)\right\}. Also the (3D) amplituhedron volume was a good one that I believe would have been a nice challenge for calculus students.
If we have a sub-forum of "challenges" and it begins accumulating lots of unanswered threads, its "appeal" increases since math people are "challenged" by problems others seem unable to solve. Also, we could move (well-posed) unanswered math threads from other math forums into the challenge forum and these posts would become more attractive (as described above) and thus fare a better chance of being answered.
Here's another one I worked on of late. Quite challenging I thought:
What can you say about:
\int_{-\infty}^{\infty}\frac{\log^{2}(1+ix^{2})-\log^{2}(1-ix^{2})}{1+x^{2}}dx
or even much, much worst: analyze the integral via the Residue Theorem.
Notice since micromass left, the math challenge sub-forum was removed. Would it be productive to start it again? I just ran into another problem today I felt was a challenge: derive a symbolic (and convergent) expression for \mathcal{L}\left\{\tan(t)\right\}. Also the (3D) amplituhedron volume was a good one that I believe would have been a nice challenge for calculus students.
If we have a sub-forum of "challenges" and it begins accumulating lots of unanswered threads, its "appeal" increases since math people are "challenged" by problems others seem unable to solve. Also, we could move (well-posed) unanswered math threads from other math forums into the challenge forum and these posts would become more attractive (as described above) and thus fare a better chance of being answered.
Here's another one I worked on of late. Quite challenging I thought:
What can you say about:
\int_{-\infty}^{\infty}\frac{\log^{2}(1+ix^{2})-\log^{2}(1-ix^{2})}{1+x^{2}}dx
or even much, much worst: analyze the integral via the Residue Theorem.
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