David Faux
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 Jul 1 comment What's the intuition behind the 2D rotation matrix? Why is it that we only need to see what the transform does to the basis vectors? Why does that guarantee that the rotation matrix work for linear combinations of those basis vectors? Jun 30 comment What's the intuition behind the 2D rotation matrix? Are there others? Apr 13 comment Why is the expected number of steps to finish this game $O(n^2)$? Oh, why does it take an infinite number of steps? Apr 8 comment How does one compute how big the cycle of modding by a prime number is? Thanks! How do I use Fermat's Little Theorem to obtain a suboptimal order? If $a^p \equiv a~mod~p$, does that imply we cycle every $p$ elements? Mar 18 comment What's the probability that Tom's bag will weigh more than Sally's? Yeah, that's what I meant. K. Mar 17 comment What's the probability that Tom's bag will weigh more than Sally's? Yeah, they're numbers. Mar 17 comment What's the probability that Tom's bag will weigh more than Sally's? Yeah, selection is without replacement. 50's relevant since I'm given the 50 weights for each person. Mar 1 comment How do I find the lowest $k$ for which a graph is $k$-partite? Oh, and all events occur within a day, so no event intervals cross 12am or span multiple days. Mar 1 comment How do I find the lowest $k$ for which a graph is $k$-partite? Ok, here's my underlying motivation. :) I'm writing a script to plan events for a conference. The times (but not the days) of each event are set in stone, so for instance, we know event $e$ must occur from 1pm to 3pm on some day. My script will determine the fewest number of days we can make the conference happen given that no events can overlap. My first attempt is to model the problem with an undirected graph with events being vertices. Edges between vertices occur if two events overlap (and thus cannot occur on the same day). Does that make the problem more feasible? Thanks! Mar 1 comment How do I find the lowest $k$ for which a graph is $k$-partite? Wow, nice! Like you said, it seems I can reduce the problem to finding the minimal number of cliques I can divide the graph into. At least the decision version of the problem is NP-complete - en.wikipedia.org/wiki/Clique_cover_problem Do you know of a dynamic programming method for solving the minimizing problem? Feb 2 comment Recurrence equation How did you get from $T(2^n-1)=T(2^{n-1}-1)+2$ to $T(n)=2\log_2(n+1)+C$? Thanks! Feb 1 comment Is $n! = o(n^n)$? Thanks! Why is $\log(3^n)=\frac{\log 3}{\log 2}\log(2^n)$ true? Dec 14 comment Why is it that $E(xy) = E(x)E(y)$ if $x$ and $y$ are uncorrelated random variables? Oh! Since then, their covariance is 0. Thanks! Dec 4 comment What's an effective way of comparing orderings? Good point. Thanks for that! Indeed, I mean permutations. Apr 7 comment Can summations distribute across absolute values? I've tried a few with holding the inside constant. It seems to work, but I'm afraid of missing a corner case. Apr 7 comment Can summations distribute across absolute values? Oh, I made a slight modification. Does it make sense now? Mar 26 comment Why does an augmented matrix with bottom-right 1 represent a system without solutions? Oh wait, but it is true if the bottom row in reduced echelon form is all 0s except for the rightmost term (which is 1). Thanks! Mar 26 comment Why does an augmented matrix with bottom-right 1 represent a system without solutions? Hmm, it seems that you're right. Perhaps what I said is not true then... Dec 8 comment Does the stationary distribution of this Markov Chain exist? Ohhh... wait, why must the probabilities sum to 1? Dec 8 comment Does the stationary distribution of this Markov Chain exist? Ah, thank you. Why does that have to be a condition?