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I
I have a problem about open or closed sets
M
Methods for approximating integrals
T
The tensor power trick
To construct exotic sets, use limiting arguments
To make a function nicer without changing it much, convolve it with an approximate delta function
To prove that a set is open or closed, use basic theorems rather than direct arguments
U
Use self-similarity to get a limit from an inferior or superior limit.
Use the implicit function theorem to prove smoothness
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Geometric view of Hölder's inequality
Diagonal arguments
Finding an interval for rational numbers with a high denominator
Try to prove a stronger result
Use self-similarity to get a limit from an inferior or superior limit.
Prove a consequence first
Lower degree by increasing dimension (or vice-versa)
Numerical optimization
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