Last night I was up until 4:30am finishing my homework for my class today. It’s the second assignment and had just 5 questions. The last question really kicked my butt for a while; it took me 8 hours on its own. The question was:
Prove that a finite ring R cannot have characteristic zero. (Hint: Begin by showing that for each element x ϵR, there must exist some positive integer kxsuch that kxx = 0R.)
I did manage to solve it, but it took a lot of tries. Basically, I ended up using a kind of proof by nested contradiction. I won’t share the details here, but after class this morning, I went to see the prof and asked him about my work (after handing it in). My logic was sound, but there was a simpler proof available which he explained. It’s actually kinda cool. The class, Math 3020 Introduction to Abstract Algebra, is all that I hoped it would be: challenging, interesting, and totally devoid of practical application! Also, I don’t have to do any computing… just reasoning and creativity. I don’t have to deal with numbers (much) – it’s much more like programming than bookkeeping. I’ve also learned to use LibreOffice Formula Editor (Math) and I love it! Yesterday I learned how to add my own custom symbols (I added a star and a not-congruent symbol).
Verity’s bicycle got stolen today. That’s a real bummer. This weekend I have to get her a new bike. It was a nice bike from MEC that cost about 800 bucks. I gotta file a police report and see about insurance cause losing that much is not cool. Also, I have to get a better lock for her next bike! I only have a short video clip of her riding it when we first got it back in April (so it was still pretty new too!) Bike thieves stealing from students are the worst. I would be okay with such thieves being dismembered. I had a beautiful bike stolen from me in my university days. It was (maybe?) a Trek 420 that I got in the very early 1990’s – probably 90 or 91. I’ll have to dig through my stuff to see if I can find photos of it somewhere…