Summer of Math Exposition

Audio is a bit muffled. Interesting topic in principle but competes with manim heavy beautiful entries, so I mark it as below average. The second half was hard to follow.

I found a new way of plotting complex numbers.

Such a nice topic. it lacks animations, the sound quality isn’t good, sometimes the pace feels rushed and it would be nice to explain some things just a bit more. I saw it’s your first video, I hope you keep doing this because even though I’ve pointed out some poor things before, the content isn’t bad at all.

The audio quality detracts from the video and should probably have been rerecorded. The sketch of the complex parabola and especially the proof at the end could have used more explanation since I had to pause to make sure I understood how you were proceeding. I think the video also could have used some more animations, even if the topic was surrounding how to manually graph these functions.

Really good video and on an interesting topic, aside from the audio issues that you no doubt know about. One criticism I can think of, is that there are certain places in the video where you refer to something on the screen. (Eg around 5:03 in the video). It’s not as though people won’t be able to find (-1,-3i) in the graph, but for me, I wasn’t able to find it fast enough and missed that whole explanation. Had to rewind a bit to see what was happening. So it may be worth adding a slide or two for highlighting the specific (-1,-3i) in a different colour so it becomes easily visible and for people to follow better. There’s a few places where it can be helpful. But all in all, really good video. Definitely look into getting a better audio setup. Even android phone mic-s work fine if you isolate in a room and add a lot of cushions around them. :)

Motivation:

I always had this sense that functions from C to C are hard to visualise as only-three-dimensional beings. This video nicely speaks directly to that issue.

Clarity:

The early parts of the video were fairly clear. It was quite difficult to follow what was going on from 4:55 onwards.

Novelty:

This video seems quite novel; I am not sufficiently knowledgeable in complex geometry or the pedagogy of complex geometry to know exactly how novel the approach being taken is, but even choosing this topic - an elementary introduction to symplectic geometry - as a topic for a maths exposition video is nice and probably fairly novel.

Memorability:

I will certainly remember the approach to visualising complex functions that was presented, as well as the picture of what shallower-magnitude slopes look like.

I think the topic you chose was nice, and I liked the whole process of questions you asked in the first 5 minutes. I think the teaching skill you have is evident, and your communication style is very clear and intuitive, but I think the video lacks quite a few things in terms of presentation and audio quality. Now I say this not to discredit, as I understand the struggles of finding a good microphone given the prices, and also how much effort it takes to find and learn a good way to present your work, especially considering how long it takes to learn manim, but I think whilst you’ve given a good shot at the way you’ve presented your work, in comparison to the very high quality of maths videos out there already, I have to say this falls short. It feels simply like a powerpoint presentation, and whilst there’s nothing inherently wrong with this, there’s better ways to present ideas with some more novelty. Also, you say at 5:35 to do one step of Newton’s method, which high school students aren’t the most familiar with until later on in their studies, but this video is also targeted at undergraduates and graduates, so I understand. I feel like I might be being a bit harsh with my rating, but I believe presentation is a very big part of the video as a whole, and I don’t want to demotivate you, because I can see a lot of potential, and I think your mic and presentation skills are the only things stopping you from producing videos that I’d rank at a 8. Overall, some very interesting ideas presented, and I really encourage you to make more videos, and it’d be amazing to watch you improve. Great work!

I’ve been curious about symplectic stuff for a while, so I was excited to watch this video… but unfortunately I don’t feel like I’ve gotten really any intuition from it. The explanation at the end (which in my view is the most interesting part) was really rushed, and it’s not clear what the point of introducing the complex plots was at the beginning… not to mention the audio quality is just so bad that it’s practically painful to watch this video.

The audio quality could have been better.

I think the formula for a Hermitian inner product at 6:30 has a typo, unless you’re writing vectors strangely.

I like your discussion of using curvilinear coordinates to graph complex functions—it seems like that’s basically what Grant did in the 3B1B video on the Riemann zeta function. I like that you also mentioned alternate methods like phase plots.

It seemed like there was a lot of text on the screen that a viewer would have to pause to read if they’re also listening at the same time.

I would have liked to see more motivation for the big picture of symplectic geometery and why to care about it.

Interesting idea in terms of visualizing the relationships in a pen-and-paper kind of way, but the motivation was tough to follow. Also audio could use work, just for future.