Methods of Mathematical Proofs

Catalog description

This course trains students on mathematical proof to deepen and broaden the knowledge of various aspect of discrete mathematics that will lay a foundation for further study of many fields in mathematics including topology, analysis, number theory, abstract algebra, probability, and computer science. Topics may include: functions and relations on sets, equivalence relations and partitions of sets, mathematical theorems and proofs, Peano Axiom and natural numbers, Cardinality and Cantor’s theorem, the barber’s Paradox and the Axiom of Choice, Countably infinite sets and Hilbert’s infinite hotel paradox, algebraic, metric and topological structures on a set. Prerequisites: MATH 2414 with a minimum grade of C.