Wordy Introduction, Motivation.

When you first start high school algebra, the big thing is FOIL-ing, right?  Factoring and factorizing quadratics.  When you get to calculus, the big things are derivatives and integrals.  Then when you get to college and start doing math, things get a little tougher.  We start learning about abstract structures, and these become increasingly specific and increasingly complex as we go along.

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