MATH 382 : Real Analysis (1)

Basic properties of the field of real numbers, completeness axiom, countable sets. Sequences and
their convergence, monotone sequence, Bolzano-Weierstrass theorem, Cauchy criterion. Basic
topological properties of the real numbers. Limit of a function, continuous functions and properties
of continuity, uniform continuity, compact sets. The derivative of a function, mean value theorem,
L'Hospital rule, Taylor theorem