Summer of Math Exposition

I'd say the biggest thing, especially in algebra heavy videos like this, is to slow down and discuss what you just derived at each step. One big missed opportunity, for example, is when you showed p(n)/q(n) is asymptotic to the ratio of the leading terms. You could've stepped back and said something along the lines of "at infinity, a rational function approaches the ratio of the leading terms. If we think to a simpler example like (4x^3)/(3x^3) --> 4/3, that makes sense, and is exactly what we would expect". Saying stuff like that makes the video much clearer, since a screen full of pure algebra is hard to digest.

It is general very good, I think it is a bit short so I would say there was time to expand more in some things for the sake of clarity.

I think the shift from black background to blue is very sudden, takes you off guard. The algebra methods look great

The premise was engaging, but most of the video consisted of algebraic calculation. I would have liked to see a more novel idea or explanation of an idea, maybe by trying to present a more intuitive proof for some of the Stolz-Cesaro theorem. Also might have been better to spend more time on the significance of functions being asymptotic rather than simply expanding on the definition.

Interesting and thorough, but it feels like it starts in the middle and then goes a little fast.

The motivation for the video is an incredibly good topic and makes the viewer curious about how the proof will be done, the animations are really good and visualise the differences between function values with graphs very well. However there is not much explanation given as to why ln(x) was choosen as a middle function for this proof which can confuse the viewer as it may not be very intuitive to people who are not aware of the subject. Overall a really good video with a great topic and proof

Phew, this video really hit the ground running. You could have started a bit more gently. A couple of sentences introduction would have been a significant help. Following the scoring guidelines, I zinged you slightly on 'motivation' for this.

I liked the visualizations, but the problem itself wasn't that interesting to me. Also I felt the proof could be done without bridging to Logarithms.

Good video. There is a small gap though. The video did not prove that “being asymptotic to” is an equivalence relation, even though it used that fact. In other words, the video did not explain why it is that “f is asymptotic to g” and “g is not asymptotic to h” together imply that “f is not asymptotic to h”.

This is a very solid video, with really nice graphics. Everything is clearly presented, and I was able to follow everything, despite not being a mathematician. My only real complaint is that there was little in the form of motivation, and everything moved a bit too quickly for my taste. Viewer's minds to to take a breath every once in a while, but the video kept speeding along without much of a rest.

motivation 5/10 clarity 5/10 novelty <5/10 memorability <5/10 i enjoyed this exposition but i thought the narration could use some breaks and less jargon or perhaps visualisations to support

Nice animations.

Excellent

a nice short video regarding a relatively easy topic. Well thought and well executed

Interesting topic that I hadn't given much thought to prior to watching the vid. I did not know the connection between harmonic series and the natural logarithm before watching. Main suggestion would be to dwell slightly longer on what H_n is before diving in. Though, that is my personal preference, and I think others would disagree.

Very clear. Nicely done.

Goal Orientation: 6/10 Novelty: 1/10 Thought-Provoking: 0/10 Comprehensibility: 5/10 Technological: 4/10 Overall Average: 3.2/10

Nice short video! One minor complaint: the proof you propose of H_n ~ log(n) does not explain much since you rely on a black-box theorem. Explaining the comparison to the integral of 1/t is very visual and can be done from scratch.