Summer of Math Exposition

The introduction and summary of the main results is very nice! I liked the discussion about error sizes; it would have been nice to see some of the things you mentioned in audio supported on the slides (like the idea that small error + tiny error = small error). I also think at the level of precision of the video, the error size formula could have been stated a bit more simply to help students parse it (epsilon_k \approx epsilon_k^p as n \to \infty rather than the limit formula that was given.) The little worked example in the spreadsheet is also a good way to make it hands on, but I think there was a missed opportunity to use the visuals from the first half in this second half so the students can visualize what the spreadsheet items mean. This would help them connect the conceptual understanding (visuals from first half) to the implementation details in the example. Maybe a Desmos applet or something similar that could combine the table with the visuals would be good for this?

Bit too complicated

The key idea of approximating the quadratic approximation by a linear function is good. But that’s really the only big insight in this video, and it takes 15 minutes of buildup to get there. I know it takes a lot more work to make a short video, but it would probably have gotten the point across more clearly.

The video addresses its title early on, but we don’t find out any more until 6 minutes in. All the background in the interim supposes the viewer is already interested in the topic, but that’s unlikely when they don’t know what the topic is yet. The viewer would be more invested if the video established early on what the question was that Muller answered.