My only take on high school math is fuck trigonometry — people who get to complex numbers can treat all of trig as a mildly interesting corollary, essentially no one else needs to know it.
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It's cool that trig introduces the sine function in the context of geometry, which later shows up in things like harmonic analysis and Fast Fourier Transforms.
Harmonic analysis and FFTs, two topics that are much easier to understand when expressed using complex numbers instead of trig functions.
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I just think it's cool to see how seemingly unrelated topics are related through math.
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My point is that they only seem unrelated because trig is taught (a) way too early and (b) badly. Teach it later and better and the topics would be obviously related, creating greater insight as a result.
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Possibly the worst thing about trig is that the way it is taught makes it seem it is about triangles, so it’s surprising when sine turns up in the study of periodic functions. If you learn it as a corollary of complex numbers, it is not surprising and in fact makes total sense.
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any suggested book that does it this way?
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I didn't know this was possible. Got an example of a good class where this is done?
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Oh, so that's the reason I had trouble with FFT. Or, it was... 1) coffee shop at midnight, 2) start homework at 2:00 AM, 3) jack daniels at 4:00 AM to fall asleep due to caffeine, 4) 8:00 AM class.
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