MAT 421: Introduction to Real Analysis I (Spring 2012)
The course MAT 421 provides an introduction to real analysis.
A tentative list of course topics is as follows:
- Definition of R (Dedekind cut), Cantor's diagonal argument.
- Convergence of sequences and series.
- Continuous and differentiable functions.
- Power series, Taylor series.
- Notions of convergence of sequences of functions.
- Lebesgue integral, measurable functions and -sets, Cantor set.
- Metric spaces, Banach spaces, Banach fixed-point theorem.
The exact course contents depend on the learning progress and the interests of
the participants. In order to support a better understanding of the topics, it
is put a strong emphasis on examples.
Literature (among many other good books on the topic):
Lecture: Wednesday, 16:00 - 17:00 and Thursday, 14:00 - 17:00
Seminar: Wednesday, 14:00 - 16:00
- Midterm 1: 30%
- Midterm 2: 30%
- Final: 40%