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Wrt imaginary numbers, just a thought: capacitance and inductance in an AC circuit.

I don't know what age group you're targeting but I found solving problems in this space gave me a great intuition for imaginary numbers; I found it quite interesting too. Heck, AC circuits are great real-world playgrounds for differential and integral equations - Laplace transforms too.

I've been fretting about how to help my kids get a better understanding of math for years. I've been bouncing between too simple and overly complicated for too long. :-(

I think I'm just going to mandate they spend some amount of time per week using Mathematica and going through some introductory book. At least they will taking baby steps in a direction better than youtube. Grumble...

So I've been fretting on which book. Any suggestions? Heh heh...

Analog electronics is a great domain, and something I want to explore more myself (I did CS, only had 1-2 analog classes, and didn't build an intuitive understanding for electricity, a gap I want to cover).

For books, I don't have a huge amount of experience but I do like the Manga Guides to X (Manga Guide to Physics, etc.). A visual medium encourages the author to rely on metaphors vs. symbolic descriptions, which I prefer in an intro to get the concepts across quickly.

How old are the kids and what do they actually like in this life?

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