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qchu.wordpress.com | ||
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almostsuremath.com
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| | | | | The aim of this post is to motivate the idea of representing probability spaces as states on a commutative algebra. We will consider how this abstract construction relates directly to classical probabilities. In the standard axiomatization of probability theory, due to Kolmogorov, the central construct is a probability space $latex {(\Omega,\mathcal F,{\mathbb P})}&fg=000000$. This consists... | |
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cronokirby.com
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| | | | | Exploring 3 different ways of encoding the natural numbers - Read more: https://cronokirby.com/posts/2020/08/encoding-the-naturals/ | |
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www.jeremykun.com
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| | | | | So far on this blog we've given some introductory notes on a few kinds of algebraic structures in mathematics (most notably groups and rings, but also monoids). Fields are the next natural step in the progression. If the reader is comfortable with rings, then a field is extremely simple to describe: they're just commutative rings with 0 and 1, where every nonzero element has a multiplicative inverse. We'll give a list of all of the properties that go into this "simple" definition in a moment, but an even more simple way to describe a field is as a place where "arithmetic makes sense. | |
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ivyfanchiang.ca
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| | | [AI summary] The author provides a comprehensive mathematical derivation of the normal distribution using multi-variable calculus and the Herschel-Maxwell theorem. | ||
