Lesson 2 is very difficult to follow because it’s not always clear what the purpose of explanations are and where the whole story is heading.
Probably moving the video Relationship between MAP, MLE and Regularization before Regularization would help. The former explains why the penalty (in the latter) is calculated the way it is; yet the former comes several units after the latter.
The Reading Frequentist vs Bayesian approach is extremely hard to digest - mostly because it’s full of calculations based on the Beta distribution’s mean, median, mode, etc. but even though you mention the Beta distribution, you don’t explain, don’t even hint to the fact that lots of formulae come from there and that the reader is not supposed to follow any of that.
I think it’s better not to show calculations if you can’t expect your readers to follow them.
I’m sure you can make your point without showing Beta’s mean, median, etc. You could simply link in Wikipedia. That would give readers the message “Look, here’s some extra if you’re interested; but for our purposes it’s not essential to understand it”.
I also think there are a couple of mistakes.
E.g. 
Did you forget the last ** or ^ sign before (1-x)?
Or 
Did you mean 
?
Thanks!