Analysis 1 Fall 2022 - Indicative syllabus

Below is the range of topics covered in the course; it may change from year to year.

Syllabus:

• Real Numbers: The archimedean property, density of \(\mathbb{Q}\) in \(\mathbb{R}\), completeness axiom, Sup and Inf, decimal expansions, countability and uncountability.
• Real and complex sequences: Convergence and divergence, sandwich test, subsequences, monotonic sequences, limsup and liminf, Bolzano-Weierstrass Theorem, Cauchy sequences, general principle of convergence.
• Real and complex series: Convergent and absolutely convergent series, comparison test for non-negative series and absolutely convergent series, alternating series test, rearranging absolutely convergent series, radius of convergence of power series, exponential series.