The best way to learn something is to teach, so they say. I find that particularly valuable. I enjoy studying and teaching, and I also try to make notes and organize my studies. More importantly, I try to make it clear and hope to write it on an easy to grasp fashion.
Please note: this is not mean as a reference textbook, but rather a summary of my studies. No commercial goal intended.
Real analysis is something I have been studying on my own for some time now. Partially because it is useful for other topics I am interested in, such as measure theory, probability and math in general. And partially because as a professional data scientist I often miss the theoretical explorations of math.
Here, I try to organize my studies, notes and thoughts on the topic of Real analysis. The material is organized as a book, and written in .tex.
Here is the list of topics I plan to organize on chapters:
- The real numbers
- Sequences and series
- Differentiation
- Integration
- Sequences and series of functions
- Basic topology
- Advanced topics
My main references I have used for studying and making these notes so far are:
- Lebl, J. (2009). Basic analysis: Introduction to real analysis.
- Abbott, S. (2001). Understanding analysis. New York: Springer.
- Rodriguez, C. (2020). Real Analysis, 18.100A | Fall 2020 | Undergraduate, Graduate. MOOC offered by MIT. Classes available on YouTube and supplementary material [here] (https://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/).
- Bressoud, D. (2022). A radical approach to real analysis (Vol. 10). American Mathematical Society.
- Wade, William R. Introduction to Analysis. Pearson Education, 2014.
- Pugh, C. C., & Pugh, C. C. (2002). Real mathematical analysis (Vol. 2011). New York/Heidelberg/Berlin: Springer.