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Norman Wildberger's "Wild Linear Algebra" series https://www.youtube.com/playlist?list=PLIljB45xT85BhzJ-oWNug1YtUjfWp1qAp https://www.youtube.com/playlist?list

Norman Wildberger's "Wild Linear Algebra" series https://www.youtube.com/playlist?list=PLIljB45xT85BhzJ-oWNug1YtUjfWp1qAp https://www.youtube.com/playlist?list=PLIljB45xT85BhzJ-oWNug... His geometry-centric approach to linear algebra was exactly what I needed to finally grok the subject. Topics like matrix multiplication and discriminants went from "why are they defined like this? it makes no sense?" to "of course that's how you multiply matrices because it's the only logical answer". It's only later that I discovered Wildberger has some ~strange~ very interesting ideas regarding imaginary numbers, but these ideas don't detract one bit from his presentation of linear algebra. Highly recommended viewing for anyone who is keen on neural networks and machine learning but struggles with understanding the underlying mathematics.

magnetomax 4y ago
Regarding imaginary numbers, I found this YouTube series really helpful to understand basics of imaginary numbers. https://www.youtube.com/watch?v=T647CGsuOVU https://www.youtube.com/watch?v=T647CGsuOVU
krackers 4y ago
It's not just imaginary numbers, the ultrafinitist rabbit hole runs deep. But there's nothing inherently wrong with it, it's just a different set of axioms than everyone else uses. With those constraints you can still do meaningful things by other means (checkout his rational trigonometry stuff), at the expense of more cumbersomeness.
robertlagrant 4y ago
His series that introduces mathematics from first principles was slightly mind-blowing to me. I don't know if it's good or not, but I kept watching!
chriswarbo 4y ago
His YouTube channel also has a bunch of other playlists. Most relevant for this topic would be the History of Mathematics course he taught at UNSW ( https://www.youtube.com/playlist?list=PL55C7C83781CF4316 https://www.youtube.com/playlist?list=PL55C7C83781CF4316 ) It covers many different fields in a shallow, introductory way (which keeps it quite approachable to non-experts). It's following a textbook, but he of course gives his own idiosyncratic takes on things.

magnetomax 4y ago

Regarding imaginary numbers, I found this YouTube series really helpful to understand basics of imaginary numbers. https://www.youtube.com/watch?v=T647CGsuOVU https://www.youtube.com/watch?v=T647CGsuOVU

krackers 4y ago

It's not just imaginary numbers, the ultrafinitist rabbit hole runs deep. But there's nothing inherently wrong with it, it's just a different set of axioms than everyone else uses. With those constraints you can still do meaningful things by other means (checkout his rational trigonometry stuff), at the expense of more cumbersomeness.

robertlagrant 4y ago

His series that introduces mathematics from first principles was slightly mind-blowing to me. I don't know if it's good or not, but I kept watching!

chriswarbo 4y ago

His YouTube channel also has a bunch of other playlists. Most relevant for this topic would be the History of Mathematics course he taught at UNSW ( https://www.youtube.com/playlist?list=PL55C7C83781CF4316 https://www.youtube.com/playlist?list=PL55C7C83781CF4316 ) It covers many different fields in a shallow, introductory way (which keeps it quite approachable to non-experts). It's following a textbook, but he of course gives his own idiosyncratic takes on things.