Summer of Math Exposition

The video is very nicely done and covers basics of induction for students who are not familiar with it. I like the visualization quite a lot.

One detail: In 1:30, you have a strange gap after $\in$ in $n \in N$.

The explanations were very easy to follow! I also really enjoyed the structure and you including both a proof via induction and one without :) Loved the Fibonacci one! I often feel like, as you said, proofs by induction don’t really reveal a deep truth about the problem (but I suspect it must be somewhere hidden in the steps? Although maybe it is also because it is often more like verifying a solution rather than finding it yourself)

Pacing was very good. Great video.

Clear explanation of how to use induction and the intuition behind it - loved it! What was really missing was an aha moment for me

As a teacher who teaches proofs I absolutely love all of the examples you covered. And the non-induction proofs for the sum of squares and the Fibonacci tilings were just brilliant. I had never seen those exact proofs/examples before and now want to share with my class. However, I found myself much more interested in the non-induction proofs than the induction proofs throughout the video. Which I suppose is partially the point as you very elegantly pointed out that in a lot of ways induction is more used to verify the answer but the way you would even get to these formulas requires something more creative. But it may be good to include more examples where the induction proof is the intuitive one (such as the proof of Euler’s characteristic formula in graph theory for example) so new students don’t get the idea that induction is never the preferred solution. Also in my experience, intro to proofs students unfortunately are not always the best with algebra. And so in order to try and isolate their understanding of induction separate from algebra it might be good to start with a completely non-algebraic more visual/intuitive induction example. That way a student who is not good at algebra would not get lost in the sauce there and think induction is really hard when in reality the core idea is super simple and accessible! I was also thinking about the algebra in the places where you skipped some steps. I completely understand why, they are not the point of the examples but I think early proofs students need to see they can verify those details for themselves. Maybe in the future try and avoid problems that require you to skip steps like that and that would circumvent the issue.

But other than that the animation was great, the overall narration flowed very nicely and this was a comprehensive overview of classroom induction. I could see it as useful for a student studying before a test after having learned induction previously to get a better perspective on it

Great video for aspiring mathematicians, or anyone who needs to learn proofs by induction. The reflections on how many of those proofs can be done without using induction. The video seems useful for people learning this for the first time. I like the rigor and the philosophy of math!