Tuesday, April 29, 2008

Recounting the Rationals

Recently I found the paper Recounting the Rationals via Mark Jason Dominus on Planet Haskell.

Mark suggests that the paper is a good first paper to read. Well since I am part way through my first Discrete Maths subject, I thought I would give it a go as my first mathematical paper to have a look at.

I was quite suprised that I could actually understand a fair bit of the paper as I read through it. It was interesting just how many of the concepts from my one Uni subject are brought together in this paper: rational numbers, sequences, trees, proof by contradiction, proof by induction and the notion of relatively prime.

I still need to spend some more time to finish exploring this paper and Brent Yorgey's six-part blog series about it. However a couple observations so far:

  • The sequence of rationals shown in the paper is quite elegant and fascinating.

  • The fact that the sequence can be represented as a tree is even more interesting.

  • Starting with sequences, switching to a tree perspective, doing a number of proofs on the tree and then relating the tree back to the sequences was a pretty cool technique.
So my verdict from the experience, is that it has been a good first paper to read. It is only 3 pages long. I could understand the paper at a high-level to start with and it has been interesting and challenging to explore in detail.

1 comment:

Brent Yorgey said...

Cool! Glad you are enjoying the paper. And my series isn't even done -- I need to get back to that at some point soon and finish up the last few posts!