Random Thoughts

[Kernel Sohcahtoa]

My abstract algebra refresher is going well: I've covered groups, fundamental theorems of groups, cyclic groups, and subgroups. I credit this appreciation to undertaking the challenge of teaching myself real analysis (this gave me plenty of opportunities to tackle proofs and to think more abstractly/generally about mathematical ideas) and to spending a good amount of time teaching myself proof writing/reading in general.  I think that I will now tackle the chapter on congruences in my number theory text and then continue my refresher of abstract algebra.  I'd like to cover the equivalent of an introductory one semester course, which typically covers the following: groups, cyclic groups, subgroups, direct products, functions, symmetric groups, equivalence relations and cosets, counting the elements of a finite group, normal subgroups, homomorphisms, rings, and fields.