I recently took a mathematical analysis course with covered topics such as convergence, continuity, derivatives, integrals, convergence of sequences and series, pointwise convergence of sequences of functions.
I contacted the author and publisher of the textbook that was used for this course and asked for their permission if I could make YouTube video tutorials using content from their book. Both parties are interested in seeing what I do and have given me temporary permission to upload a handful of videos (privately) so they can look through and approve them for becoming public videos.
My question to the math teaching community is: What is the best approach to teaching proof-heavy material on YouTube?
I am initially inclined to follow exactly what Khan Academy does. But most of the videos on this website are not exactly proof-heavy. The material I want to attack can be abstract. Should I follow what KA does in their YouTube videos or is there a better way to enhance these videos for understanding abstract math analysis?