September 2010 S M T W T F S « Aug 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Categories
- Mathematics (42)
- Arithmetic (2)
- Combinatorics and Probability (12)
- Lotteries (2)
- Markov Chains (10)
- Cryptography (3)
- Differential Equations (6)
- General Applied Statistics (1)
- Group Theory (1)
- Linear Algebra (6)
- Music (1)
- Textbooks (26)
- Munkres's Topology (26)
- Set Theory and Logic (25)
- Functions (5)
- Relations (15)
- Equivalence Relations (5)
- Order Relations (10)
- The Integers and the Real Numbers (5)
- Set Theory and Logic (25)
- Munkres's Topology (26)
- Poetry (8)
- Love (1)
- Mexico (1)
- Guadalajara (1)
- Miscellaneous (4)
- Nature (4)
- Mathematics (42)
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Author Archives: Carlos
On Lanchester’s Differential Equations and WWII: Modeling the Iwo Jima battle
Almost at the end of World War II, a battle to the death between US and Japanese forces took place off Japan in the island of Iwo Jima. We can definitely apply a Lanchesterian analysis to this encounter; in fact, … Continue reading
On Stochastic Processes
Why can’t I shake the feeling that a stochastic process really… isn’t? In previous posts we have been able to frame a deterministic system in terms of its Markov transform matrix, and going backward really doesn’t seem like a problem. … Continue reading
On Lanchester’s Differential Equations and their Transform into a Markov Transition Matrix (or, the Markovization of the Lanchester Equations)
I have been very curious as to whether the Markovization of differential equations is applicable to all systems, linear or not. In the case of the SIR differential equations, Markovization was possible even when the system is both non-linear and … Continue reading
On the Swine Flu (a Year-and-a-Half Later)
This week I have been revisiting the swine flu scare of April 2009. The Mexican government then was particularly anxious: it suspended regular classes, and many kids were just thrilled that they found themselves suddenly on vacation. Some schools even … Continue reading
On the SIR Equations and Their Transform into a Markov Transition Matrix (or, the Markovization of the SIR Model)
It’s been a while since I’ve had the time to write here, mostly for personal reasons. However this period has not been without very exciting “discoveries,” at least in my mathematics understanding. Ever since last year in April with the … Continue reading
On Markov Chain Music
Ever wonder what music produced by a Markov chain might sound like? Yeah, me too! …and… wonder no more! So I went to where the piano is and grabbed the more regular, simple score I could find. As it turns … Continue reading
Posted in Combinatorics and Probability, Markov Chains, Mathematics, Music
Tagged Markov chain, Markov chains, Mozart, Music
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On the Beale Cipher, Part III
In this post I’m including a compressed archive of some results I have obtained by following through on my previous post: I used the Declaration of Independence transition probability matrix I calculated based on a text I found online, and … Continue reading
On the Beale Cipher, Part II (and Other Book Ciphers)
Last time I talked about extending the usual frequency analysis on the (first) Beale cipher to augment our understanding of the composition of the individual letters the numbers may represent. I have said before that Markov chains are immensely applicable … Continue reading
On the Beale Cipher, Part I
Ugh, so right now there is construction going on behind my house; an abandoned house got put down and I can only imagine Telecable extending it’s dominions over. The street is zoned to be residential, not commercial, but the owner … Continue reading
On revolutionizing the whole of Linear Algebra, Markov Chain Theory, Group Theory… and all of Mathematics
I have been so remiss about writing here lately! I’m so sorry! There are several good reasons for this, believe me. Among them: (1) I have been enthralled with deciphering a two hundred-year old code, the Beale cipher part I, … Continue reading