Summer of Math Exposition

Great explanation! As far as suggestions go, I would recommend polishing the editing. The screen is filled with equations after only 1 minute into the video which could scare students off. Instead you could transition (animate) from one equation to the other while you’re explaining. Otherwise, this was a very informative video! Very articulate and well explained.

Excellent video for the most part, but the part involving g(z) and T was really hard to follow and understand by comparison.

This was a good overview of a root-finding algorithm that I had not seen before. The introduction made me think that this would focus on real-valued functions, so I was a bit surprised that it was a complex approach. The reason why the circle test works wasn’t entirely clear to me.

This is a really great video on this topic. The circle test should’ve taken a little more time and a few more examples but it’s great.

This is a good video but it is a little above my knowledge base. However, I think it is cool how we can use a circle to solve a problem that doesn’t seem to involve a circle at all. I can tell this is well organized and explained wwell. Nice work!

this was honestly a really great video: an interesting new algorithm and pretty and clear visuals, with code and references ! good job :)

This wasn’t a bad video, but I don’t think it is all that well motivated. I think I followed everything, but I’m not sure why I should care, and I think the target audience will feel similarly. In addition, while the creator did use some nice graphs to help clarify things, this “video” was essentially just a lecture. In the future, I recommend that creator to think deeply about how to use the medium of video to do things that can’t be done in a lecture.

Very well explained. I didn’t know about this method before, but by the end of the video I had a clear understanding of how it works and why. I also really appreciated that you mentioned the original work where this method was first proposed, as well as the way you introduced the topic.

Interesting algorithm, and the video looks well edited and polished overall. The part that felt too magical for me was the Schur-Cohn Test (8:42 to 12:13) and I had to watch it several times. Why does T(g(0)) < 0 imply that there’s a root? I guess 11:45 sort of hinted the product of roots but it felt not completely fleshed out. Also what if I keep applying T(T(T(T(T…T(g(0))…)))) and it’s always positive and never exactly zero? Can it happen? For me, if the Schur-Cohn test was better explained without any lingering questions then I can see myself giving a higher score.

The AI voice causes problems in my language, but the main issue is that you created a video that simulates a traditional frontal lecture. There are too many formulas on the same screen, which makes it not very useful for students, or at least excludes many of them.

Very interesting piece of mathematics that I hadn’t heard of before! Thanks for sharing.

I like how you walked through the familiar quadratic formula as a hook for the viewer—it would have been cool to flash the cubic and quartic formulas on screen to give an extra clear sense of how hard purely analytical rootfinding can get!

I would suggest inverting the pacing somewhat when discussing the annulus convergence search vs. the circle test. In my opinion, the existence and function of a reliable circle test is much more surprising/interesting than the fact that gradually narrowing in on a root will produce increasingly accurate estimates. The whole time I was watching the convergence demonstration, I was wondering “Wait… but what are we actually testing?”

The test was also challenging for me to understand with written equations alone. It reminds me somewhat of the technique of conformal mapping in complex analysis (common in the heat transfer/fluid mechanics world to turn ugly domain shapes into canonical/trivial ones like half planes, circles, etc.), and I think both these concepts would be most powerfully demonstrated with visuals/animations to really show what the transformation is doing (especially the repeated applications of T, which were hard to follow/reason about).

I loved the code visualization/exploration of the convergence! Reminds me of those rotating circle chains to demonstrate Fourier decomposition of 2D line art. Super fun!

This exposition did a wonderful job of describing this method of root finding AND used the visuals very effectively! The transition from a bisection method (very simple) to the method being discussed (more complex) really drew me in and was not superficial. The use of specific examples clarified more abstract general algorithm in a meaningful way. I think it was accessible to all the audiences tagged.

I learn something from this video, especially about what is going on geometrically and that’s my favorite way to more deeply understand mathematics. I could see a series of videos discussing various root finding methods being a wonderful way to teach about root finding in general - including context, pros and cons, etc.

The flow was very good between the dialog and the visuals. The only thing that might have been better is having accurate scales for the specifics - halving and quartering the circle sizes. Of course, this may have had other visual issues - things in diagrams getting too small or too large.

I enjoyed the algorithm, and the explanation of the main idea. Perhaps narrowing the audience would improve the flow and would help to keep the level of presentation more constant. What i mean is that you spend time deriving the quadratic equation but this must be “trivial” to most people, but then the difficulty in the video increases greatly (in particular, in the explanation of the circle test). I would’ve liked if there were more time explaining the circle test and why it works.