Yes, yes, I know. At this rate, my weekly recap will become bi-weekly. I didn't do a lot the week before last, owing to Victoria Day making for a shortened week. So rather than two very short blog posts, I decided to forbear and write one short blog post instead.

The last two weeks have been more reading, more learning, and a little thinking. I hesitate to ascribe a label like "productive," since it's hard to quantify. I think I understand my problem now, but there remains a lot for me to learn in order to start trying solutions.

I tried running the original algorithm for computing the spreading number, which was written in CoCoA, on my computer. I had hoped that my 2 GB of RAM and 1.83 GHz processor would have enough memory to compute some additional numbers. Alas, CoCoA stubbornly crashed (after several long hours) each time I instructed it to do so.

So I ported the code to Macaulay2. It's even slower, which makes me suspicious that I'm missing something--after all, I am learning both languages, so I'm sure that in transliterating the code I managed to miss an obvious way to make it more efficient. Still, it looks like the original algorithm won't produce many more useful results, at least not until I stick it on SHARCNET.

My supervising prof pointed me to a series of lectures he gave on combinatoric commutative algebra. Last week I started working through those, and I'll continue doing so this week. He's given me several promising "leads," I suppose you'd call them, but at this point, I have to start exploring avenues of interest and seeing if they produce any interesting results. I've already toyed with some alternative approaches in Macaulay2, familiarizing myself more with the language, but I think I need more experience with the mathematics first.

Probably the most significant news of the past two weeks would be my decision to attend the Canadian Undergraduate Mathematics Conference at the University of Waterloo and the Combinatorics & Optimization Summer School preceding it. Initially I was reluctant to go, because I don't like to travel, but Aaron and (maybe) Rachael are going, so I won't be alone. Plus, I'll get to visit my grandparents. That's July 5-10, a few more weeks away. Until then . . . time for more learning.