This course will examine, through careful reading and extensive discussion, key issues in mathematical studies. Topics explored include number, figure, extension, relation, magnitude, multitude, continuous and discrete quantities, definitions, postulates, axioms, hypotheses, theorems, proofs, proportions, equations, measurement, limits, infinity, and the certainty and exactitude of mathematical knowledge. Readings may include, but are not limited to, works from Apollonius, Euclid, Archimedes, Nicomachus, Newton, Euler, Frege, Hogben, Hardy, and Lieber. Using threaded discussions, written posted assignments, and online peer collaborative projects, the student will develop thinking, reading, and communication skills.