Summer of Math Exposition

This video is a nice refresher on some of the fascinating properties of pascal’s triangle, but I feel like, otherwise, there’s a lot more improvement that can be done. The video does not define pascal’s triangle, for example, seemingly expecting the audience to know what it is; before going over its main utility when that would likely already be known by many who do know about Pascal’s triangle. Particularly given the “graduate”-level tag.

Also, on a video production note, audio balancing between narration and the intermittent music could be improved.

That being said, narration is clear and walkthrough is fairly detailed. I think I would have just liked a more unique topic, than something generally overdone on the internet.

Opening creation of the triangle should show more steps of the creation, cuts to the full triangle for only a split second and then we wait at “Part 1” title text. Pascal’s triangle and binomial coefficients were known long before Newton (he is credited for expanding to the infinite series version). Nonstandard notation F_(k+1)P(n) is confusing, it’s not a product, and the indexing isn’t directly shown through examples.

The combinatorial interpretation of this coefficient (n choose k) actually counting something is completely left out.

I don’t see why you would use that notation for binomial coefficients instead of the standard one. If a student is learning about this subject, they might get confused with your notation. Also, I think you should have included the formula to calculate the coefficients, it’s very important. The video is just too incomplete to call it a “deep dive”.