- Write down the problem.
- Think real hard.
- Write down the solution.
From the Bahamas
Back from a 5 day cruise from the Bahamas, stopping in Half Moon Cay and Nassau. There were some beautiful places there, but more importantly it was utterly relaxing. The inevitable explosion of memories from BSM was also delayed a little as I was constantly distracted with other fun stuff.
Now back to some regular postings,
- I posted my review for the BSM algebra exam in the hopes that it would help people. It is available here or under the “About Me” page.
- I really want to do a Clash of Clans math review sometimes this winter break…
- An investigation into the irrationality of trig functions from a lattice point of view? We’ll see if I have the time.
Lost to History
As my time at Budapest comes to a close, I can’t help but be reminded of the times during honor band in high school.
For three days, sixty other musicians and you gel together and make beautiful music for the sake of music. Friendships are made, and is inevitably short-lived with the nature of gathering students from all over the state. During the last rehearsal of one such honor band, the conductor said something quite profound to me. He told me to look around and know that this is the last time this group of people will be assembled. Consequently, that was also the last time that particular sound associated with the ensemble was made in history.
After the concert, the sound of the ensemble is forever lost to history.
I guess BSM, or any other camp for that matter, is something like that. That group of people will never be together again, and that synergy of relationships will be gone after the program. But as the saying goes, it is better to have loved than not loved at all.
And so, another happy chapter comes to a close in my life.
Cube
Floating Cube Illusion from Intel on Vimeo.
Oscar Wilde
“There are only two tragedies in life: one is not getting what one wants, and the other is getting it.”
Kygo – Firestone
Done!
Done with my internship! I’m in Montana right now.
Log of Determinant
This should be a well known methodology by now, but it seems to not be.
In statistical work, one frequently sees the expression 
where the absolute value means determinant of covariance matrix 
. With large covariances, the calculations can easily overflow, but usually the finally value is a reasonable finite number.
The covariance is key, as it allows us to compute a Cholesky decomposition of 
first, which is quite numerically stable. We will have two triangular matrices whose determinants are the products of their diagonals (proof left as an exercise to the reader). Taking the log of that will transform the product to a sum!
Thus 
where 
is the diagonals of the matrices. You’ll find that this will rarely overflow, and possibly (depending on how sophisticated the determinant calculation is) speed up the work!
The Voyage of Life
I went to the National Gallery today to take a final look before I leave next week. This particular series of painting caught my eye, especially the one above.
It just seems to reflect the drastic kick of reality I’ve been ingesting. When I was little, dreams were so lofty, ideas so wild and thoughts run carelessly. Now, the future seems perilous at times… what if my next steps are wrong?
I’m still looking forward to the next year though…. but what lies after Cornell truly scares me.
New Project
I’m starting to write solutions for the Larson’s problem book on Github. It’s just a small project I would like to keep adding on to it as I progress through the book…
Link is here: https://github.com/runiteking1/larsons_solution