Much of mathematics relies on our ability to be able to solve equations,
if not in explicit exact forms, then at least in being able to
establish the existence of solutions. To do this requires a knowledge of
so-called "analysis", which in many respects is just Calculus in very
general settings. The foundations for this work are commenced in Real
Analysis, a course that develops this basic material in a systematic and
rigorous manner in the context of real-valued functions of a real
variable. Topics covered are: Basic set theory. The real numbers and
their basic properties. Sequences: convergence, sub-sequences, Cauchy
sequences. Open, closed, and compact sets of real numbers. Continuous
functions and uniform continuity. The Riemann integral. Differentiation
and Mean Value theorems. The Fundamental Theorem of Calculus. Series.
Power series and Taylor series. Convergence of sequences and series of
functions.

- Teacher: Dr. Javed Hussain