Summer of Math Exposition

Not great audio. Great and relatable intro, but the visuals went down a bit after that.

1-9 Motivation: 2 Useful, more food the merrier! Clarity: 8 (very clear, I personally really liked that you skipped talking about the math of each situation and didn’t include a graph for duration of events 1-5, however, doing so does slightly take away from the clarity of the presentation) Novelty: 1 Memorability: 1

score 12/4=3

The subject is interesting and the explanations are fine although they remain very lecture-like and this may be a bit terse for a video.

The video is often in advance compared to the voice. It made me disconnect and follow the text and not so much the voice.

I was very interested in the subject matter. Please send more time explaining the optimal strategies for both examples. The introduction of matroids was intriguing. Please spend more time explaining the connection between matroids and optimization.

TLDR: Cool video. Love the concept, but presentation could be better: You should explain things with concrete examples before getting abstract, be more concrete with your examples, visualize more, and use visuals as an aid to your voiceover rather than an info-dump/distraction

Way too much going on with the animations when you start the knapsack problem. The huge wall of text is overwhelming. Animations should supplement the voiceover, but in this case it distracts from them. You did a good job of this with the food explaining the problem visually. You should’ve made a similar visualization for the problem, maybe you’re looting looting, mining, etc. and can only hold so much, and you show all the items and a weak little character that couldn’t possibly hold all of that. Visuals and concrete examples help, you went fully abstract with just numbers immediately. It helps to start concrete before you get abstract.

Also, when showing the algorithms run on knapsack, you should show the live counter of how much value you have and how much weight you have on you. A bar filling up to max and turning red would be a good example. Reduces the cognitive load on the viewer.

Jumping right to the proof is also overwhelming and too much too fast. We go from simple problems to sets and subsets and weird properties. Slow down, get concrete first, establish more motivation. Start with exchange argument with the food example, and then mention the theorem. And either explain the theorem in its entirety and more slowly, or just reference it without trying to go into it. I think just referencing it would’ve sufficed for what seems to be the goal of the video, and cutting out any mention of sets would reduce unnecessary abstraction to make it easier to understand

I wasn’t convinced by your explanation of the exchange argument. You basically said “could a better solution exist? If it did, then greedy would’ve not been optimal, which is impossible. therefore greedy is optimal.” The core of an exchange argument is the exchange phase (explaining how a different optimal solution could be turned into the greedy solution without losing optimality) which you didn’t include.

Nitpicks

use a declicker for voiceover audio, your mouth sounds are distracting. This is a pet peeve of mine, so I’m not sure if normal people are bothered by it as much as I am lol.

the university student maximizing free food example is great! I love it, brings me back. But I was a bit confused bc at first I thought the bar size was the quantity of food. Instead of having $Food_n$, it would’ve been clearer to have named events and have a clear labeled time axis with ticks for hours or something. Also here’s a LaTeX tip: for something like $Food_n$, you should write it like \text{Food}_n to make $\text{Food}_n$

Simply explained, and straight-forward. Also, free food is always a good motivator…

1. During the discussion of the knapsack problem, it felt that there were some unanswered questions: What algorithm do we use to get the optimal solution? Why doesn’t the greedy solution work?
2. The Rado-Edmonds theorem felt under-exposited? Maybe the how and why the two properties work could have been explained much better and more clearly, going beyond the example.

Animations were amazing! Presentation was great! I liked your voice!

I think that you were able to fit a lot into a short ammount of time and that the conent was very interesting. However, I think that the video could have benefited from going more in depth for a longer time. For example, you could have maybe gone more in depth as to how the argument is generalized to matroids from the example. Also, there maybe could have been an example showing why the set of possible solutions forms a matroid. Overall, what you have is great but it needs more.

It is a nice little teaser, but for my taste the video would benefit from taking a little more time with clarifying the examples.

The whole video was not really well-explained, especially the Knapsack problem. For people who have not heard of this problem at all (like me) it is not clear what the value $W$ is and how it is computed or what the rules of the problem even are. Also structure wise, I think it would probably have been better to group the parts of the original food problem together, so put the proof that the greedy algorithm is optimal in this case before the discussion of the Knapsack problem.