I have a newfound respect for algebra. I was reading Dummit and Foote during the break of orchestra today, and I found something really neat. One might wonder why rings are commutative under addition. So here’s the reason: Let a and b be elements of a ring with a 1. Then (1+1)(a+b)=1(a+b)+1(a+b)=a+b+a+b. But (1+1)(a+b)=(1+1)a+(1+1)b=a+a+b+b, so b+a=a+b. I wonder why Agboola didn’t mention it in class. It’s far too neat to ignore, in my opinion.
I ran my first Math Jam today. I think that it went pretty well considering that it was my first time. I was a bit stunned at the beginning when no one really said what I had expected them to say, but after I got over that initial shock, I think most of my decisions were pretty good. The first problem took a bit longer than expected, and as a result, I rushed through the second one a bit too quickly and was left was much more time than was needed for the third problem. I tried to slow the pace down a bit but was unable to do so effectively. After the Math Jam was finished, people started asking for bonus questions, and the only thing I could think of off the top of my head was the Lindelöf Hypothesis, which was slightly unfair. Fortunately, Richard had a better question which was from an IMO. Somehow that seems slightly more appropriate.