This is not a textbook. Okay, you ask, what is it, then? These are notes I use when teaching a class. But it looks like a textbook. A two-semester sequence on modern algebra ought to introduce students to the fundamental aspects of groups and rings. That’s already a bite more than most can chew, and I have difficulty covering even the stuff I think is necessary.
Unfortunately, almost every algebra text I’ve encountered spends far too much effort in the first 50–100 pages with material that is not algebra. The usual culprit is number theory, but it is by no means the sole offender. Who has that kind of time? Then there’s the whole argument about whether to start with groups, rings, semigroups, or monoids.
Desiring a mix of simplicity and utility, I decided to write some notes that would get me into groups as soon as possible. You still haven’t explained why it looks like a textbook. That’s because I wanted to organize, edit, rearrange, modify, and extend my notes easily. I also wanted them in digital form so I could read them and would be less likely to lose them.
I used a software program called Lyx, which builds on LATEX.
