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1d
comment Using probability to detect exam cheating (identical wrong answers)
What's interesting is that most multiple choice quizzes are just like that, except when the teacher takes special effort to hide the right answer or does a nasty thing of the kind $\sqrt 7$ is closest to a) 2.6456 b) 2.6457 c) 2.6458 d) 2.6459 (to which any normal person should just respond "and who would care remembering it with this precision or seeing one of them as any different from the other three?") :-)
1d
answered Using probability to detect exam cheating (identical wrong answers)
1d
comment “Advice to young mathematicians”
If the question is to be understood literally, the answer is "No, I wouldn't mind." If you prefer me to answer the implied question rather than the formal one, can you, please, be more specific? @nayrb I spent 3 hours today in the classroom (preparing people for qualifiers) showing how a problem solving process is akin to the bargaining on the market (we did 4 reasonably hard problems in measure theory), but do you really expect me to post a transcript of my crazy spiel here? The most I can do (if I have a long evening with nothing else to do) is to choose one problem and to go over it...
2d
awarded  Constituent
Dec
17
comment A conjectural inequality of the form $\int_a^b g(B'_1(t)) dt \le \int_a^b g(B'_2(t)) dt $ with convex increasing $g$
It is a finite process when $B_1$ is piecewise linear, so it is completely rigorous in that case. The general case follows by approximation as soon as you show that the piecewise linear functions inscribed into the graph of $B_1$ converge to $B_1$ in a strong enough sense to justify passing to the limit in the integral. In general, "a proof" is not as much a formal argument as a clear mental picture translated into a comprehensible language, and the ability to translate just comes with training and experience. :-)
Dec
17
comment A conjectural inequality of the form $\int_a^b g(B'_1(t)) dt \le \int_a^b g(B'_2(t)) dt $ with convex increasing $g$
Or, even simpler, make the area over the top graph of stone, the area over the bottom one of paper, take scissors, and start cutting pieces off the area over the bottom graph carefully avoiding the stone. Translate what you see into induction/limits/whatever other math. dialect you like.
Dec
16
awarded  Caucus
Nov
28
comment Poincare type inequality on compact manifold
What exactly do you mean? You can always add constants without changing the derivative, be it the Euclidean space or the compact manifold, so the offset by the value at some point (or the mean over the ball, or whatever else killing the constant terms) is inevitable on the left hand side.
Nov
28
comment Does this type of function exist?
It is not even true in general if we have just radial limits and that's exactly when Baire comes to the rescue. If it is bounded around zero, it is just a boring exercise about removable singularities and you seemed to have absolutely no problem with it from the start :-).
Nov
28
comment Does this type of function exist?
Baire Category Theorem is the full name (it is just a very smart way to use the nested interval lemma). The answer to your second question is that my ingenuity is insufficient for that, but you can never guarantee that the elementary approach does not exist. All I can guarantee is that it cannot be too simple because of the reason I mentioned in the end of my post.
Nov
28
answered conformal mapping, regions of the complex plane marked +/-, find the function f,
Nov
28
comment Integral/infinite sum related to Bessels which pop up in optical coherence theory
An explicit formula is certainly out of question here but we can discuss the ways to compute it quickly with decent accuracy though in that case more information is needed (range of arguments, precision, etc.)
Nov
28
answered Does this type of function exist?
Oct
6
awarded  Nice Answer
Jul
5
awarded  Yearling
Jul
1
comment Question about Riemann Mapping theorem
It means that if $f,g$ are any two mappings with $f(z_0)=g(z_0)=0$ and positive real $f'(z_0)$ and $g'(z_0)$ (a priori completely unrelated), then $f=g$ everywhere (so $f'=g'$ as well, etc.). As a side note, it would be nice to have some language ministry (or whatever it is called in your part of the world) to establish some canonical way of spelling "Riemann" for its constituents so that the poor outsiders would not have to guess if Reimann and Remiann is the same person or not ;)
Jun
16
comment Irreducibility of $x^n-x-1$ over $\mathbb Q$
This is outlandishly clever! Make sure it gets included into some textbook or lecture notes :-)
Jun
16
comment Consider convergence of series: $\sum_{n=1}^{\infty}\sin\left[\pi\left(2+\sqrt{3}\right)^n\right]$
What you had in your head when writing this was impeccable. What you wrote in the last few lines is total gibberish.
Jun
15
comment Solving $a^2+b^2\equiv 0$ mod $c$ for distinct integers $a,b,c$ constrained between two consecutive squares
$\frac{x^2+y^2}{c}<\frac{2\cdot(2n)^2}{n^2}=8$
Jun
15
comment Solving $a^2+b^2\equiv 0$ mod $c$ for distinct integers $a,b,c$ constrained between two consecutive squares
Hmmm... I have the desire that is exactly opposite to yours: can you tell how you used a computer here?