Random Thoughts

[Kernel Sohcahtoa]

I just finished working an exercise in my abstract algebra book that ultimately required me to make use of a main theorem in the section I was studying (namely homomorphisms and normal subgroups) along with a corollary from a preceding chapter on normal subgroups and a main theorem in the chapter on homomorphisms.  It felt good to harmonize mathematical ideas in order to achieve the goal of the proof.  Having completed that exercise along with a few more in that chapter, I'm finished studying groups: I have gained an elementary understanding of the material, which was my goal; I have also gained a great appreciation for the material.   Thus,  it is time to move on to rings and just give myself a basic understanding.  I'm looking forward to beginning this topic tomorrow.