Summer of Math Exposition

Very nice video!

Around timestamp 3:20 the video claims that having a single root in an interval implies the function is one-to-one on that interval. This is not correct, and a simple counterexample is f(x) = x^2 - x on the interval [-1/4, 3/4].

Brent's method and plasma physics are both great topics, but it's a bit jarring when halfway through the topic jumps from approximating roots of functions to electronic energy levels. It might make sense to reverse the order, and to only invoke Brent's method once the context demands it.

The presentation is great, the content requires high focus. I don't say this as a negative point but this is not for people looking for edutainment

Straightforward explanation of the method and interesting application.

This has been quite a refreshing take on numerical analysis. The author truly took the time to animate + motivate the algorithm being studied. The application to plasma physics was also a great addition to the video. Quite well done. Wish I had you as a numerical analysis lecturer. If I would have any feedback, I would have loved to see the application of Brent's method first, as in the motivating through plasma physics. Then, get into the nitty gritty of the algorithm.

The humour was noted and appreciated. I understood what was being said, but not why it was being said. Compression of the concepts led to a couple of claims being made that felt a little unsatisfactory. I'd love to see this as a series, because it's such an interesting topic, but I find the concepts quite hard to grasp on a first watchthrough

It would be nice if the conditions that determine when to use which method would be stated and maybe also explained.

I can readily imagine this as a Numberphile video - seems like a sister video to Stirling's approximation. And after the gas example, I could imagine it as a Sixty Symbols video too.

I had already seen this video and I am subscribed to the channel. The content is interesting, the script and the animations are great, although the video is a bit too long for my personal standard

Very well explained and visualized. Didn't know about this method until now!

I think this is one of the best videos I've seen using the PPT style of presenting. I also do enjoy it when topics like this are tied into chemistry.

This is a very solid video. The basics of Brent's method were clearly explained, and the video had really nice graphics. My two critiques would be that some of the text was rather large, which was a bit distracting. More substantively, the introduction of the Saha equation was a bit jolting. I understand why it wasn't derived, but it still detracted somewhat from the overall quality of the video.

Does quick overview instead of actually explaining conditions when to fall off into quadratic or secant.

Yeah great video but i was still unable to understand the physics example would be great if you included a more simpler example but otherwise great video