Over the years I’ve occasionally chanced upon “things” about these topics that I wished I could have shared with more people. While many of them have been spoken of elsewhere, others haven’t generally been publicized on the web/blogsphere. Of course, others no doubt would have thought of or come across ideas similar to what I would be blogging about; so I definitely do not assert any claims of being the first to discover them. But I do feel that there would be some people interested in reading about them.

Even if I turn out to be the only one reading this blog, there’s a very good reason why I should still do it — it would help improve my clarity on the things I feel important enough to share with others. Steve Yegge wrote a neat post explaining just this. Dear reader, if you don’t blog (for whatever reasons), you should at least consider reading that.

A bit on the timing: I’d been thinking of starting a blog for quite some time now (all the while “gathering” interesting material to speak about), and my sabbatical (this whole of December) have given the nudge I needed to finally start one.

Till you come ’round again, here’s a little problem from IMO to ponder on: If is defined from such that for each , then prove that for each . For another interesting problem involving the solution to a functional equation, check out TAOCP Exercise 1.2.4 — 49.