A Course in Real Analysis ... in Marimo!
My current project is to develop the “reference section” of a course in real analysis.
https://axiomtutor.github.io/acira/
When the reference section is sufficiently complete, I’ll start working on the “front end”, i.e. a pedagogical section which is intended to simulate a full university course. It should eventually have lectures, exercises, exams, and demonstrations.
The intent is to present all of the information in a standard university course on real analysis, although I cannot help but incorporate a few design features that I don’t see represented elsewhere.
Reference / Pedagogy Dichotomy
One is: A separation of reference and pedagogical material. I think too often, having reference and pedagogy in the same place, confuses readers about exactly what they’re supposed to do or learn from a given text. Sometimes they are meant to understand what the author is saying deeply, on a first reading.
But sometimes, the author is merely showing the reader something so novel and complicated, a newcomer could not possibly understand it deeply or reproduce these methods on their own. This often happens in challenging proofs of theorems. The author intends the reader to merely be exposed to something new, and eventually warm up to it over time. But the reader doesn’t know that.
Therefore I am trying to keep these separate, with the pedagogical section meant to explain to students what they are expected to understand. The reference section is meant to merely hold a dense collection of information, which the student should not expect to understand immediately. But the density and organization of the information can be a virtue, especially after having processed the more conversational and introductory pedagogical section.
Marimo
I’m trying to implement a lot of these ideas in Marimo notebooks as much as possible. I’m hoping this gives opportunities for interactive widgets, demonstrations, and quizzes.
Lecture Videos
I’ll also hopefully incorporation presentations in video for, perhaps at the final stage of developing this project.