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mattbaker.blog
| | 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...
| | rjlipton.com
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| | A result on the prime divisors of polynomial values Cropped from source Issai Schur was a mathematician who obtained his doctorate over a hundred years ago. He was a student of the great group theorist Ferdinand Frobenius. Schur worked in various areas and proved many deep results, including some theorems in basic number theory. Today...
| | jaydaigle.net
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| | We continue our exploration of what numbers are, and where mathematicians keep finding weird ones. In the first three parts we extended the natural numbers in two ways: algebraically and analytically. Those approaches gave overlapping but distinct sets of numbers. This week we combine them to get the complex numbers, and see some hints of why the complex numbers are so useful-and so frustrating.
| | blog.lambdaclass.com
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| Introduction When working with cryptographic applications you need to understand some of the underlying math (at least, if you want to do things properly). For example, the RSA cryptographic system (which was one of the earliest methods and most widely adopted, until it lost ground to better methods, such as