Real Analysis

This course was developed by me around 2025, but is no longer taught. This page was made to archive some good material of this course, and I would like to teach it again some day.

Catalog description

Introduction to mathematical analysis with the objective of being able to understanding and writing proofs. Topics include: Basic set theory and real numbers. Convergence of sequences and series of real numbers. Continuity, differentiability, and Riemann integral of single variable functions. Sequences of functions and interchange of limit operations. Metric spaces, topology, and convergence properties.

The material of this course was developed based on the book Basic Analysis: Introduction to Real Analysis by Jiří Lebl, and the course 18.100A provided by MIT.

Lecture slides

1. Basic set theory

2. Real numbers

3. Sequences

4. Series

5. Continuous functions

6. Derivative

7. Riemann integral

8. Sequences of functions

9. Metric spaces

The full set of slides is available as one PDF file here.

Course reader

The course reader is one PDF file consisting of a cover page together with the lecture slides (in 2up format).