My first thought when registering for this course was, "It's algebra, how hard can it be?" The complexities of ring theory, however, proved both difficult and intriguing. Attempting to classify groups of numbers and proving that specific groups of numbers belong to a certain classification is all an art form. This could easily have been a memorization-heavy class, but we were able to write the definitions of everything on a notes sheet before tests, so the course instead emphasized logic and reasoning, similar to the proofs-heavy MATH 300. Overall, 402 was an sneak peak into the world that contemporary algebra research is currently focused, and it pointed out how much complexity we can pile on "elementary" math concepts.