Every year there are quite a few students who want to learn more than the regular courses can offer them, so they find a faculty advisor and create an independent study. Sometimes it’s truly created by the student, with the advisor only as a “guide on the side,” and sometimes it’s a structured one-on-one course designed and planned by the advisor. This year I’m working with three students in the latter model.
Actually, two of these students are working with me and a colleague together, so it’s two-on-two, which I guess simplifies to one-on-one if we believe in such ratios. Two very advanced freshmen are studying the first half of the world’s best math book, Excursions in Calculus: An Interplay of the Continuous and the Discrete, by Robert M. Young. Despite the title, not much of this book is about calculus. It’s mostly about number theory…and algebra, and geometry, and probability, and fractals, and lots of other topics, both continuous and discrete. I highly recommend this amazing book. My two students are doing a great job with it.
My other independent study is with a sophomore who is interested in linguistics and comes in with a surprisingly broad and deep sense of language. So I am more-or-less repeating what I did last year with two seniors, one of whom is now a freshman at Georgetown and the other of whom is now a freshman at William & Mary, as well as three years ago with a then high-school senior who is now a junior at Carleton. I always enjoy these experiences, as I otherwise get very little opportunity to talk about linguistics these days.