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bio website hilbertthm90.wordpress.com
location Seattle, WA
age 27
visits member for 3 years, 7 months
seen 1 hour ago

I'm a sixth year grad student studying algebraic/arithmetic geometry.


12h
comment Computing the genus in positive characteristic
It seems likely that you won't be able to "rule out" wild ramification ... because depending on the degree $d$ there will be cases where you do have wild ramification. I remember doing this problem a few years ago and found it fun and enlightening. I'll play around with it later today to see if I remember how it goes.
Apr
12
comment Is (the proof of) Fermat's last theorem completely, utterly, totally accepted like $3+4=7$?
@DonAntonio I think maybe you are underestimating the amount of math research done every year. The Math Reviews (which only reviews actual published stuff!!) puts up about 86,000 publications per year. I assure you most of that is vetted by far less than 100 people. In the context of the question, one would never write "if this result is true" of those published papers read by maybe one other person, and hence one would definitely not write that for FLT which has been vetted much more thoroughly.
Apr
12
comment Is (the proof of) Fermat's last theorem completely, utterly, totally accepted like $3+4=7$?
@DonAntonio Suppose only 100 people really understand it. Wouldn't you agree that 100 people is way more than most proofs that come out? Most theorems are fairly insignificant and the person that wrote it plus maybe a referee plus maybe 1 or 2 other people read them. The prominence and significance of FLT makes it much more widely read and understood than most other theorems proved in the last 50 years (also the Taylor-Wiles part is pretty "basic" stuff by today's standards, I'm not referring to the full modularity theorem).
Apr
12
comment Is (the proof of) Fermat's last theorem completely, utterly, totally accepted like $3+4=7$?
I think there is such a thing as degree of belief in a proof, because there could always be some unnoticed mistake (this has happened throughout history). In the case of FLT, this has actually been checked and understood by such a vast number of people in comparison to most proofs that I'd have as much confidence in it as something like the Fundamental Theorem of Calculus. I would definitely not make that type of caveat which would probably be perceived as quite insulting to those that have checked the proof.
Apr
11
awarded  Notable Question
Apr
10
comment Why must average only be used with normal distribution?
I'm not sure the answer to your question. It may have been unclear on the spot feedback and not what they really meant. I know several reasons why the interviewer would not like that answer though. Think of a low frequency wave. You will audibly only hear one note, but averaging small time interval samples would give you values that increased and then decreased. This would lead you to believe that visually something should be going on, but in reality there is nothing audibly going on.
Apr
5
comment Find the distribution of $W$
Sorry again. It visually looks like the max happens at 1/2, but I think it is actually skewed and not symmetrical, so the mean is probably different: wolframalpha.com/input/?i=plot%28exp%28-x%5E2%2F2%29*int%28exp%28-t%5‌​E2%2F2%29%2C+t%3D-infinity..x%29%29
Apr
5
comment Find the distribution of $W$
Sorry to drag this conversation out even more, but while falling asleep last night I realized why this is what we should expect to see. We would expect a large amount of the time that $Y-X>0$ happens because $Y>0$ and $X<0$, so we set $W$ to the positive value. We would expect a large amount of the time that $Y-X<0$ to happen because $Y<0$ and $X>0$. Thus when we set $W=-Y$ we are more often switching the sign to positive and hence it skews to the right of $0$.
Apr
5
comment Find the distribution of $W$
Neat. I just plotted this answer with wolfram alpha and it is exactly what my experiment shows. That is so completely bizarre that it centers at 1/2 like that. The description seems so symmetrical...
Apr
5
comment Find the distribution of $W$
I was just guessing based on 100,000 plotted points. After several trials it looks very much like it is centered at 1/2, but I'm not sure what the actual distribution is.
Apr
4
comment Find the distribution of $W$
I'm confused where the squared term went. Shouldn't the answer be $F(w)^2$?
Apr
4
comment Find the distribution of $W$
Maybe its OK if you just change $dydx$ to $dxdy$? Still, something is wrong.
Apr
3
comment Find the distribution of $W$
Something is weird about those integrals. Should the inner one of the first one have limits $-\infty$ and $x$ or something?
Apr
3
comment Find the distribution of $W$
I thought the answer should obviously be $N(0,1)$, but I just wrote some quick code to test that guess and it looks like $N(1/2, 1)$, which I find strange. I'm not a great programmer, so maybe I made a mistake somewhere ...
Mar
31
comment Name of decision method in which probability of taking an action is exactly past successes / past attempts, while alternative actions normalize
For example, I blogged about this recently where I used the beta distribution to update my beliefs about the bias of a coin after each flip and make guesses about whether or not it would come up heads or tails, but that analysis led to the exact update rule you propose: hilbertthm90.wordpress.com/2014/03/19/decision-theory-2
Mar
31
comment Name of decision method in which probability of taking an action is exactly past successes / past attempts, while alternative actions normalize
Actually, I'm being dumb. This is exactly what is called the Naive Bayes Classifier, but usually you would read off the probabilities from a training set all at once. This is just a conversion of that algorithm to fit into a decision theory framework. Often times your rule is exactly what pops out of a more complicated form of analysis where you estimate discrete values with a continuous distribution (like the beta for determining the bias of a coin).
Mar
31
comment Name of decision method in which probability of taking an action is exactly past successes / past attempts, while alternative actions normalize
This is basically just a discrete Bayesian decision model. I'm not sure I've seen exactly your update rule, but the general process can be made with any probability distributions.
Mar
29
comment Why are mathematicians more interested in elliptic curves than other algebraic curves?
I'm kind of curious whether the premise is true. Are mathematicians more interested in them?
Mar
27
comment Cohomology of the structure sheaf of $\mathbb{P}^1 \times \mathbb{P}^1$
Do you know Serre duality and the canonical bundle?
Mar
26
comment Can likelihood be changed when the prior changes?
I think this is a Bayesian/frequentist divide. If you use a classical statistical test, then the likelihood does not depend on anything except the data. If you use a prior, then it does and is equal to the other case with a uniform prior (as your graph shows).