Summer of Math Exposition

That was nice! It’s rare to see something that could work 1-to-1 the same on YouTube as in a classroom without having to change the format.

And I like the mix of pre-made slides and handwritten notes! Many people go too far in one direction.

I step into this topic recently. It’s interesting, but I’d like to see an original approach, with remarkable examples for students and memorizable charts. Anyway, this is something I can propose to my student.

I like the initial hook of the video and how it build overtime to more complex ideas. It’s a shame you couldn’t get a justification for the derangement formula, but it’s a tough one! The visuals were simple but effective, although I would make labels and details larger in case people are watching on smaller devices.

I also think it’s worth having a clear idea in mind of who the target audience will be, although it’s tough for something like this without a classroom context. It feels like students ready to think about Taylor series would be comfortable enough with probability trees that the section could be shortened somewhat, although I appreciate the full explanations for everything :)

As expected with you being a teacher, I think your presentation style is fairly well-developed, which is a positive. That said, a lot of your analysis here is really ad hoc: I don’t think its good to be promoting the idea that a sequence has to approach a special number and that can be determined by taking important numbers in math and guessing (especially given how many high-school level students have built up conditioning that they should just do random operations on numbers when they don’t know what to do) or that patterns that hold for small values like the ones in your table necessarily keep holding, and given that the concept of derangements is so key to what you’re doing here, just dropping the formula in with no justification doesn’t really feel like an explanation to me.

I’m trying to give you some credit for presenting a novel piece of math in a way which represents a realistic line of inquiry, and I do think I learned something interesting when I did go look up derangements to try to understand that formula, but I think the explanation in this video isn’t quite there, and could even perpetuate some misunderstandings.

Not a very engaging video. Doesn’t explain the derivation of the derangement counting expression, making its conclusion circular and hand wavey. Duh, n! * 1/e divided by n! is 1/e. Why if you didnt know beforehand it converged to 1/e, how would it be tackled?

Anyway, the motivation is clear enough but not well rewarded. Its pretty clear what he talks about, and the concept was novel enough.

There was no mindblow, that’s the tragedy, it had a good set up too. He even mentioned hes a masters in stats, and never uses any stats to derive the crucial expression. He just goes, here it is.

couldve been worse, couldve been better.

The video gives an interesting example of the appearing of e in a simple situation but the first time it came to us is with a try an error with “important numbers” as if it was kind of a list of them. It doesn’t provide a complete intuition about why we should try with this number in that specific situation like you should try with pi if you see a circle. it doesn’t provide the fully explanation of why is the number e there. only use the Taylor definition of e in the end to almost check that the calculation is correct.

The same happens with Dn which formula is given and checked and not deduced.

Highly interesting! Would have been interesting to see where the magic lim sum … = e^x comes from. Hope to see that in another video. :)

The problem was well-motivated. It makes the viewer curious about how e shows up in a situation where it’s not expected. But the formula for the number of derangements just pops out of nowhere. I think you should derive the formula somehow. Explain where it came from and how someone can find it on their own.