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gilkalai.wordpress.com
| | algorithmsoup.wordpress.com
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| | The ``probabilistic method'' is the art of applying probabilistic thinking to non-probabilistic problems. Applications of the probabilistic method often feel like magic. Here is my favorite example: Theorem (Erdös, 1965). Call a set $latex {X}&fg=000000$ sum-free if for all $latex {a, b \in X}&fg=000000$, we have $latex {a + b \not\in X}&fg=000000$. For any finite...
| | rjlipton.com
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| | We must know. We will know---David Hilbert Mihai Prunescu is at the Institute of Mathematics of the Romanian Academy. He works in logic and complexity theory. We recently discussed his work on Hilbert's Tenth. Today we thought we would do a follow up discussion of a recent paper of his on the famous Hilbert's Tenth...
| | fabricebaudoin.blog
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| | Here are the lecture notes of the minicourse given at NYU Abu Dhabi. DirichletDownload
| | 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...