Real Analysis, Class of 2024-2025
- Text book: Elementary Real Analysis by Thomson and Bruckner.
- Lecture notes
- Handwritten notes
- Time: Sundays, 3pm-5pm, Phnom Penh time.
The aim of this class is to make an introductory course to Real Analysis. We start from a reasonably ground setup; by assuming the existence of the set \(\mathbb{R}\) and its Completeness Property. From here, we will learn some basic definitions after which we will start developing the notion of limits, continuity, integration, differentiation, series, et cetera.
TD (Exercises)
Part 1: The real numbers
Here we assume the existence of the set so called \(\mathbb{R}\) that is bigger that the set of rational numbers \(\mathbb{Q}\) in the sense that \(\mathbb{R}\) also contains the irrational numbers like \(\sqrt{2}, \pi, \ln 2\) et cetera. A mathematical way to describe this is that:
Property: The set \(\mathbb{R}\) is a superset of \(\mathbb{Q}\) and it satisfies the completeness property.
