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Critical analysis of Euclidean geometry from transformational, algebraic, and synthetic perspectives. Coordinate and vector geometry relating transformational geometry to linear algebra. Informal study of historical development of Euclidean and non-Euclidean geometries and the questions relating to the parallel postulate to develop understanding of axiomatic systems. Offered fall and winter semesters. Prerequisites: MTH 210 and either MTH 204 or MTH 322.