3blue1brownMath language and expressions
Most of us know that e is used as a common base for expressing exponential relationships, but why? In particular, why do we need to convert from any other base to base e? What does this conversion allows us to do? And how to understand the mechanics of such conversion? We will explore these questions in this video. Through this journey you will gain a deeper understanding about the special properties of math languages, a topic which we rarely think about. After this video you will see how the difficult concepts of e, log are naturally connected.
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2.9
Unsure who the intended audience is, given the topic itself is fairly introductory, but you briefly invoke the binomial theorem.
3
Be more engaging, more dynamic.
6.2
This is a nice video. The topic is well explained, and the graphics are nice, but there is nothing to really distinguish it from many others. So, even though I liked it, it isn't all that much better than most that I've seen.
5.7
While I think that the video is fine overall, I wonder about the target demographic of this, as well as how clear the main point of the video is conveyed.
After watching the video, my understanding is that the main purpose of the video is to explain why it is useful to switch to the natural basis (e) when dealing with exponential growth. But at the very beginning I got the impression that you would instead talk about why the letter "e" is used to represent this number. While a pretty minor detail it is something worth noting in my opinion, as subtle word choice can have a big effect on how something being said can be slightly misinterpreted.
If I understand the intention correctly, this video presupposes that the viewer has worked on exponential expressions and is comfortable with how switching between bases works. But in this case I would suspect that the viewer would also have an intuitively clear idea of why it is practical to do all the work in a standard basis, just based on their own experience. Moreover, it's not like we HAVE to switch bases when working with exponential growth, as long as the base we're working with is the same in the problem we're working on the need to convert is often diminished. Moreover, we may choose to use any positive number except for 1 as the "standard" basis. So the question we should be asking is "why the number e in particular"?
Furthermore, I wonder how well some concrete points are conveyed in the video. For instance, I wonder about the part where logarithms are brought in. Now, I know from before what a logarithm is, so I get how they work beforehand. But I'm not so sure that it would be easy for me to process what was going on between 3:44 and and 5:18 in the video and what that had to do with anything being presented so far in the video.