Fundamental Math Systems, aka math of elementary ed majors. --- x is an irrational number if and only if the set { nx mod 1 | n is a natural number } is dense in [0,1].
Alright! You'll have to tell us how it goes. --- I thought I saw upon the stair a little man who wasn't there. He wasn't there again today. Oh how I wish he'd go away.
(Also work/reconstruction are slowing down and I got through Chapter 1; that was really good; notes to follow)
(Also, the original on-topic comment wasn't merely an excuse to post that; I actually had come in just to post "Yeah, you show em!" as a weird non-sequitur) --- Set signature in options page.
Got back about half-an-hour ago and now I am super-tired, although I didn't feel tired right after the lecture. The adrenaline, I guess?
On the plus side, the class is great. About 30 or so students - most of them traditional college undergrads, but a couple of adult students, too. I felt that I had a pretty good rapport with them overall. The first section I did was logic, so we started going through the usual truth tables and started on slightly more complicated compound statements. When I stopped to take questions, one guy was pretty honest and said that he had no idea what was going on, which I really appreciated, actually. So I went back and explained it again, this time using a few more examples, and by the end they were able to fill in the truth tables pretty well on their own.
I'm jumping into elementary set theory next class. I'm really excited for everything that I hope to cover, because this is really the kind of math that I feel should be introduced way early on in middle school. In summary, first class was excellent and I'm looking forward to the rest of them!
As for you, Wil, thank you for reading, as always, and I definitely look forward to another email from you. Those always make my day. --- x is an irrational number if and only if the set { nx mod 1 | n is a natural number } is dense in [0,1].
That's great that you had a student so openly ask for help on the first day. Challenging your students while making them feel comfortable enough to admit their confusion seems like the ideal situation. Hope the semester/quarter/whatever goes over well. --- Ocarinakid