Lead Faculty: Dr. Igor Yakov Subbotin
Prerequisite
MTH 223
Course Description
A look at sets, functions and the real numbers as an ordered set. Topics include the Completeness axiom, cardinality and Cantor's Theorem; sequences, subsequences, monitonicity and boundedness; the Bolzano-Weierstrass Theorem, LimSup and LimInf; topology of R1 and R2; open sets and limit points. Also discusses compactness and the Heine-Borel Theorem; the properties of continuous functions, uniform continuity, the mean-value Theorem, inverse functions and differentiability; the Riemann integral and the Lebesgue Measure.