Linear Algebra: Lecture 1/33 - Introduction to Complex Numbers

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Additionally, problem sets for this video series can be found here:

Divergence is Divergence

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That was great! I'm so glad I decided to review this material. Not only that you've provided it but your ability to convey the topic is inspirational. I never made the connection to the degree you've displayed with Euler's formula and then his identity. Truly fascinating and well done! You might want to consider making that small section a separate video. I bet that would bring a lot of traffic to your tutorials. It was like a mystery unfolding. Very impressive!

Cheers

mbike

Thank you for your kind and good lecture. It feels like a one-on-one lecture, so I understand it well.

wpcbfvc

Thank you so much for posting free education videos ❤

devpardhan

The complex numbers obey field axioms (group ops, closure, etc), but I guess in your case that's assuming a construction of the real numbers (which I haven't been through). The insight is that complex numbers were recognized in part because of violations of closure, to which you allude. Perhaps in this comment I'm just recommending your numbers and sets or group theory series. Maybe you recorded the LA series before numbers/sets and/or groups, but now they're available. I think that's where students should start with your lectures if rigor is important.

I like the way you speed up when writing lengthy statements and erasing the board, which is kind to your audience. One instructor I encountered created 100+ hours of presentations on linear algebra and was still going step by step through row operations in seeking eigenvalues and eigenvectors, rather than assuming students could perform the computation themselves.

I have no pretension of instructing anyone in mathematics -- I'm an autodidact, but not a teacher; I can imagine how difficult it is to prepare lectures and present the development logically, trying not to omit material required in later lectures. Here, I can see it's not easy to get to Euler's formula at this level if we (for example) have to construct the real numbers first (for those power series)! Thanks for your efforts.

danieljulian

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