Re:A few of the best math explainers from this summer [video]
by Evgenii1 on Sunday October 24, 2021 @06:13PM
(#28982416)
Wildberger's channel for me has the best 'explainers', he reinterprets math and in the process you end up learning about both the standard definition and a different model he comes up with for example in his FMP playlist is a totally wild reinterpretation of the complex numbers using Dihedron algebra https://www.youtube.com/playlist?list=PLIljB45xT85Bfc-S4WHvT...
I always like seeing standard math curriculum cast to some other interpretation for example E.T. Jaynes book 'Probability Theory the Logic of Science' the first few chapters he builds up from scratch probability theory deriving it entirely from quantitative logic using a running example of a robot being programmed using sampling theory and hypothesis testing, parameter estimation and performing random experiments. No Venn diagrams, the Bernoulli urn rule comes popping out as a logical consequence, the central limit theorem reveals itself as a special case when you discover a phenomenon over the chapters where all other distributions seem to gravitate towards a gaussian/normal distribution which he proposes renaming the central distribution then there's even an entire chapter on where the names for these distributions come from and how they are misleading. No measure theory either, you expand a continuous function to a finite orthogonal function, you assign probabilities in a finite dimensional space, do the probability calculation then pass to the limit at the end where you end up using the Lebesgue integral in what he claims is 'it's original meaning'.
Anyone who knows of more books or channels that do this I'd be interested
I always like seeing standard math curriculum cast to some other interpretation for example E.T. Jaynes book 'Probability Theory the Logic of Science' the first few chapters he builds up from scratch probability theory deriving it entirely from quantitative logic using a running example of a robot being programmed using sampling theory and hypothesis testing, parameter estimation and performing random experiments. No Venn diagrams, the Bernoulli urn rule comes popping out as a logical consequence, the central limit theorem reveals itself as a special case when you discover a phenomenon over the chapters where all other distributions seem to gravitate towards a gaussian/normal distribution which he proposes renaming the central distribution then there's even an entire chapter on where the names for these distributions come from and how they are misleading. No measure theory either, you expand a continuous function to a finite orthogonal function, you assign probabilities in a finite dimensional space, do the probability calculation then pass to the limit at the end where you end up using the Lebesgue integral in what he claims is 'it's original meaning'.
Anyone who knows of more books or channels that do this I'd be interested
https://www.youtube.com/watch?v=60z_hpEAtD8
https://www.youtube.com/playlist?list=PLnQX-jgAF5pTkwtUuVpqS...
https://docs.google.com/spreadsheets/d/1fswG7v8wKFoK06ilbF9V...
he's pretty fast ;)