Induction explained by International Math Olympiad Bronze Medalist: The Essence of Induction part 1 скачать в хорошем качестве

Induction explained by International Math Olympiad Bronze Medalist: The Essence of Induction part 1

This is the math video explainer I made for 3Blue1Brown's summer of math exposition contest. The topic here is mathematical induction and it's aimed at high schoolers and college students first encountering this topic. My goal here wasn't to formally state what induction is and then try to hammer in the definition through examples. Rather the idea was let's solve a problem where the way you'd describe your solution is via "building up from smaller solutions". This is the essence of what induction is trying to accomplish. This is a famous problem for introducing induction, but it's usually presented in a way that's incredibly out of the blue solution. It doesn't cover the question: "Why induction?" and that's especially problematic when someone is trying to learn induction for the first time. In the end I don't think I've hit my mark with what I wanted to do with this video (I could've made more of the animations and could've spent more time explaining what it means for us to "solve" n=3, 4, which we didn't really formally do). However on the other hand it's a cool introduction without focusing too much on the proof writing aspect of the problem (we can cover that in future videos). The idea was that this informal treatment can help build up some of the intuition for what induction is in essence. I made the music semi-seriously, but while putting the voice and the animations together I saw how crucial the music was to the whole experience. Figuring out how to install manim, use it, making the animations, and finally giving the animation some voice and music took about 7 days to make.