PMATH 333 - Introduction to Real Analysis

This course is designed to enable students who did not take the MATH147/MATH148/MATH247 sequence of advanced calculus courses to fill in the missing gaps from analysis needed to prepare them for studying further topics in analysis in PMATH351/PMATH352. Topics discussed include: completeness of the real numbers, supremum and infimum, sequences and the Bolzano-Weierstrass theorem; the topology of Euclidean space: open, closed, connected, and compact sets, the intermediate value theorem, the Heine-Borel theorem, and the extreme value theorem; continuity and uniform continuity, sequences of functions and uniform convergence; the Riemann integral over rectangles and the integrability of continuous functions.