Summer of Math Exposition

You have structured the topic in a completely logical and understandable way. There are no special aha moments (at least in my opinion) and you’re video style (Using Manim with a black background) is pretty average which is why I didn’t gave you 10 points but that shouldn’t bother you to much. For simply understanding the topic, you’re video was great!

I would definitely agree this topic is a key one which doesn’t get enough attention, and the explanation here was really well thought-through. You commented on the dryness of the subject - I think the style here made it engaging, but maybe referencing some specific applications or linking to an explanation of contravariance/covariance would be beneficial?

The pacing was really nice. Maybe a bit fast in the end because there’s a lot more to cover, but it’s perfect as an intro because it motivates the problem and starts from the bottom. Maybe it would have been even better to cut some of the things in the beginning (like polar coordinates etc) to jump more directly to the main topic.

Anyway it is usually a hard topic and a lot of students struggle with it. This video really helps to introduce them with known problems. Thanks for the difficult work it suppose to make these kind of videos.

I’ll start by saying I liked the video and I can see how this would be very useful to people studying physics. Here’s the constructive criticism:

I would have cut the original text of Einstein’s paper. I don’t like when videos include long stretches of quotes. The self-deprecation tells me that you also know this is boring and easy to tune out. I would only include boring quotes if you are making an important point about the boringness, and I’d wait until later to make sure I’d earned the viewer’s attention.

I think you spent too much time on the basic vector review and not enough time on the Einstein notation. I was lost for a while at the triangle visual, for example; it wasn’t clear how the numbers on the triangle mapped to the indices of $\epsilon$. Moving the position of the 1, 2, and 3 nodes was confusing. If I understand this correctly, you can get the right result by drawing those nodes in the starting position, and just drawing the first arrow can tell you if you’re moving clockwise or counterclockwise. If I’m wrong, that’s still a sign that you should have spent more time explaining it :P

I believe that if you had a few more weeks, you could have found a better way to explain how to multiply those Levi-Civita symbols.

It is clear, but the Einstein convention on indeces itself is easy to understand. I miss the purpose of this video, this conveniention is not teached at school. Anyway, it’s a good frontal lesson, just add some memorising techniques.

as said in introduction this is a dry matter, but it is fully necessary to learn. to hav ethis in a 10 minutes video format (plus exercises) is relly nice, as students can watch several times if needed. Well done !

Good video. Maybe more interesting and captivating for advanced high school students or early undergrad, but the material is pretty dry. To be fair it dealt with it really well, and I would have benefited from this video when first attending university. However, compared to other SOME videos, not my favourite.

Good video. I like how the video transitions from one topic to another, building on previous ones and has clear animations.

Here’s my constructive feedback:

1. There were some parts which felt rushed or could use some visual, intuitive explanations. For example, when dot products were introduced, they could have used a little more deep dive and built up
2. Some parts missed answering the “why?”. For example, around 8:00-9:00, video mentions that a_i * b_i is frequently encountered, but not a_i * b_i * c_i. But we never get to know why
3. Since this video is tagged for “high-school”, I would say the video could have been made more beginner friendly by explainig some of the later concepts more gradually. Also, the explanations in the second half of the video were a bit dry. Could have used more visuals.

I enjoyed what the video was conveying, but it seems nothing related to Einstein.

Well, I just watched a video about notations and somehow the 15 minutes flew by without me noticing. So that is a very impressive feat! What hooked me was teasing how this notation can help with vector calculus and topics like electromagnetism. Sadly the video never goes back to an actual application of the notation, besides the proof running in the background at the end of the value. I would have like some more applications and example problems solved on screen.

This video was fun to watch, I don’t think this topic is widely covered so good choice. I think it comes out a bit too dry because of lack of explicit examples. For future videos, I recommend the creator include a motivating example or a work-out example that would make the experience more memorable to the viewer. Still, the content is properly and correctly presented.