In the Winter Quarter of 1977, just a few days after my 21st birthday, I started attending a class in Abstract Algebra, taught by Ted Tracewell at Cal State Hayward, now known as Cal State East Bay. Sad to say, I can find no pictures of him, but the celebrities who look most like him are the science fiction author Isaac Asimov without the muttonchops, or the songwriter/playwright/actor Adolph Green with glasses.
I just turned 66, and I now can identify that class as the one that changed my life. I show pictures of Asimov and Green smiling because that is how I remember Ted Tracewell. He had a real excitement about higher mathematics and it always shown through. When I taught, I tried to emulate that enthusiasm when I could, and some students commented on it. Some said they hated math, but because they saw I loved it, it made it easier to get through the class.
Many topics in group theory feel like solving puzzles, both the proofs and the exercises, like filling in Cayley tables and finding conjugacy classes, which I have shown on the blog. More puzzle-like topics include representing finite abelian groups, representing groups pictorially in terms of their generators the structure of normal groups and filling in character tables, the last topic part of group representation theory. The inter-connectivity of group theory makes it hard for me to figure out the order in which topics should be introduced.
I will often take side trips to talk about the lives of the mathematicians who made important discoveries, but today it's my personal history, important to me, if no one else.
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