math 3640 8645 modern geometry course description axiomatic systems finite geometries modern foundations of euclidean geometry hyperbolic and other non euclidean geometries projective geometry 3 credits prerequisites math 2230 math ...
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...Math modern geometry course description axiomatic systems finite geometries foundations of euclidean hyperbolic and other non projective credits prerequisites or equivalent mathematical maturity overview content purpose the objectives are twofold a to introduce student rich variety geometric topics beyond those studied at high school level this should prove valuable mathematics in broadening his horizons specifically prospective teacher by increasing knowledge area b help develop skills logical reasoning use method careful presentation proof may transition from more manipulative courses freshman sophomore abstract advanced major consistency completeness independence an system critique euclid s elements set axioms for role parallel postulate absolute c discovery on some theorems poincare model d ecliptic circles theory inversions verification introduction methods class will be presented lecture form with questions discussion encouraged textbook greenberg marvin jay th ed new york w h fr...