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Complex Dual Numbers Construction

The Complex Numbers are pretty well known, but their infinitesimal cousin, the Dual Numbers, is much less popular. However, I thought it would be interesting to combine the two into a single structure, but soon found there are multiple ways to achieve this depending on the exact properties you would want. With the first definition, the i and epsilon components do not commute, but in the second definition they do. You decide which is more exciting to you!

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2.99 Overall score*

133 Rank

6 Votes

5 Comments

Comments

3.8

Would be way cooler if you had some more graphics in the video, would give it more dynamics. Otherwise, your methods are nice, would be cool to show more parallels with the complex numbers in the beginning of the video, so that people who are not familiar with it would get it, also would be great to give some historical background, as to why people even came up with dual numbers

3.4

The paper itself is really interesting, and I definitely learned some math from it. When you write a paper, the details of the calculations are the most important part. But when you're presenting it in a video like this, focus on the intuition, not the formalism. I trust that the algebra works out, I just want to know why you're doing it.

1.1

I'm rating this as "notably worse" than most of the math videos that I have seen (and I watch a lot of them). Before I begin I would like to apologise for giving you this rating. I don't enjoy writing things to people that might hurt their feelings. Here are some constructive comments 1. This video just consisted of you reading out your paper. A math video should be more than that. 2. As a video I found it harder to follow than if I had just been reading your paper. You kept on scrolling up and down while you talked. So often I would be reading something and then suddenly I found it was off screen. 3. At one point (I didn't take note of the time but it was around 25:00) you kept saying how tedious the algebra was. A word of advice: If you find your subject boring your viewers will too. Find a way to make it more interesting.

2.5

First off, best of luck with your qualifying exams! This may be personal preference, but I would have preferred this submission as a non-video submission. It is an interesting topic, but in a video format, I like to have derivations slowly revealed to me. Out of the four guidelines for scoring submissions, I felt as though the 'motivation' would be the easiest way to improve the video. You clearly know your stuff and the step-by-step derivation was clear. I imagine that a punchier intro would really allow this channel grow.

Pros : - The subject is original and seems like it could actually have cool applications in math education (a bit like hyperreals to teach calculus). Cons : - A bit too informal, there are times where you hesitate a lot while speaking, or find typos in the visual support. Those could have been edited out/taken care of. - You should try to motivate better why what you are presenting in useful, place it in a more general context, give the intuition about the objects you are working on (i.e. the link between dual numbers and infinitesimals) in the first few minutes of the video. - You do a lot of "vocal algebra" and the notation is quite heavy. I understand you have to get in the nitty gritty algebraic details. But maybe there is a way to show that while still keeping the video "palatable" for a less experimented viewer?