Quadratic Extension Fields
and
Geometric Impossibilities

Abstract: These are some lecture notes for a junior-senior level course in abstract algebra which was based on Hungerford's book Abstract Algebra, an Introduction. The idea was to move quickly, assuming only minimal preparation, to a concrete development of quadratic extensions of the rationals and the attendant discussion of the classical impossible ruler and compass constructions. The development borrows heavily from the first chapter of C.R. Haddock's beautiful little book Field Theory and its Classical Problems, Carus Monographs #15, Math. Assn. of America, 1978.

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