Sunday, August 06, 2006

Light Reading Leads to a Dead End

My light reading on topology has detoured into recreational math. I'm trying to come up with activities and projects for one of my fall classes, and I was hoping to do something with paradromic rings. These are not "rings" in the sense of a set with two binary operations that satisfy a list of axioms; rather, it's in the sense of borromean rings. Which is to say: not something that I've thought about much before.

What are paradromic rings, you might ask? Well, it's hard to find out much about them. You can find their definition. A google search reveals that hobbyists and undergraduates have thought about them a bit. There are two pages in a Dover book.

However, real mathematicians who we take seriously have not given them much thought:

I could spend a few hours figuring out their basic properties, proving things, all that. But I'm sure that someone else has done that before, and I would rather just read what they've done. And I'd like for my students to be able to refer to non-internet sources when doing their write-ups. The math that's most accessible to undergraduates is also the hardest to find. On Monday I may have to track down a reference librarian.