Recently in math/cs Category

Ola niños. Hope you recover from the shock of seeing a new entry on this blog. Haven't been here in a while. Looks like this is all still up and running. I'm surprised I still remember my mt password.

So why this entry ? Well, I've done another thing I haven't done in a while: I wrote yet another note in LaTeX solving some simple problem in a pompous way. I used Scala to implement the solution. Scala is coming along nicely, it feels natural to me and it has some powerful abstractions and features. There's definitely a buzz about it. A book on it is now available, the Eclipse plugin behaves well and there are open source projects that use it.

Before I get completely rusty with LaTeX, here's another one in the series of absurdly trivial papers: this one derives a program that establishes if there are 4 points from a set of points on a circle that form a rectangle.

Got these from the scala mailing list: interesting functional programming algorithms (scala enthusiasts are porting them over from haskell)

Finger Trees: A Simple General-purpose Data Structure

Bryan Ford. Packrat Parsing: a Practical Linear-Time Algorithm with Backtracking. Master's Thesis, MIT, 2002.

This blog has just hired a new editor-in-chief Nadia.
She started Oct. 15th (7.2 lb and 20.5 inches) and has already had a positive impact on the site: the blog has been upgraded to mt 3.2, the photos slideshow page has a new thumbnail viewer on the right side when viewing albums, the papers section has a new entry and the blog links sidebar has been cleaned up and has a couple of new additions. But even Nadia admits in a recent interview with "Blog Editors-In-Chief Magazine" that unless she hires new staff writers not much content will come to this blog in the next couple of months.

So in the meantime here's another edition of "piles of cool stuff". A lot of time has passed since the last edition so many cool things accumulated on the observer desk but unfortunately a lot of things were also lost again because they were not recorded right away. What remains is:

• Eric Hehner's "A Practical Theory of Programming" is now available online for free.
• If you understand Spanish here is another cool book about program calculus and algorithm derivation available online for free.
• If you study or teach linear algebra this paper has a very modern example of how wonderfully applicable math is: linear algebra is behind the Google search engine's power to do relevance ranking. The paper is very well written with clear explanations, descriptive examples and exercises. Simply excellent.

With this theorem taken from "Elementary Number Theory in Nine Chapters" by James J. Tattersall (p. 204, Theorem 6.20) we can choose m and p such that f(x) = x^m mod(p) is bijective: choose m and p so gcd(m, p - 1) = 1.

To convince yourself that f is not always bijective try m = 5 and p = 11 for an example with lots of collisions.