Summer of Math Exposition

Very well done, impressive animations and exposition.

Hi ! I absolutely love your video, the animations are beautiful, your pace is really good, each scene is well balanced with the right amount of formulas, text and visualizations. Just to nitpick, I would say that the topic of the video is very well known from a lot of undergrad students, so revisiting it is not that original. However, I think you managed to make the best video on this topic by far ! Another thing is that you could probably improve your audio quality, but it is already very decent. Maybe also add a little bit of music, and you'll have the perfect videos ! Thanks for your work and for submitting this wonderful presentation.

I really enjoyed seeing your individual based simulations matching up quite well with the logistic growth and Lotka Volterra predictions. For me, that was the most interesting part of the video. It would have been nice if more was made about the link between your simulation and the differential equations which approximate the behaviour of the simulations. When they matched up well it felt a little like plausible magic to me. I also think that this submission would benefit from being more homogeneous in the level of prerequisite knowledge that is assumed. You start by explaining differentiation from first principles, but later on you don't explain more advanced topics in the same detail, such as infinite series, orbits and velocities in phase space etc. I personally think it would be better to just assume that your audience knows about derivatives, and to point those that dont know to a source which explains derivatives as a prerequisite to this video. This lets the audience know from the beginning the rough level of knowledge they will need to understand the video.

Overall, a very good and well-executed introduction for advanced high school to lower university students. If there is one area where this video is not as strong, it is that the topic is not that novel. One errata: at around 2:00 the equation is shown with f(h) rather than f(x). Also, the English I am familiar with uses the soft 'g' in 'logistic'. As a physicist, I was a little disappointed that you didn't take the opportunity around 18:00 when you stated there is an invariant quantity, to relate this to other fields which use differential equations such as mechanics.

Great Video

Very interesting. Covers a lot of ground without feeling overwhelming.

Simple explanation of a rather complex topic. Well done.