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mattbaker.blog | ||
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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... | |
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fabricebaudoin.blog
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| | | | | In this lecture, we studySobolev inequalities on Dirichlet spaces. The approach we develop is related to Hardy-Littlewood-Sobolev theory The link between the Hardy-Littlewood-Sobolev theory and heat kernel upper bounds is due to Varopoulos, but the proof I give below I learnt it from my colleague RodrigoBañuelos. It bypasses the Marcinkiewicz interpolation theorem,that was originally used... | |
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thatsmaths.com
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| | | | | The Riemann Hypothesis Perhaps the greatest unsolved problem in mathematics is to explain the distribution of the prime numbers. The overall ``thinning out'' of the primes less than some number $latex {N}&fg=000000$, as $latex {N}&fg=000000$ increases, is well understood, and is demonstrated by the Prime Number Theorem (PNT). In its simplest form, PNT states that... | |
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jeremykun.com
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| | | Hard to believe Sanjeev Arora and his coauthors consider it"a basic tool [that should be] taught to all algorithms students together with divide-and-conquer, dynamic programming, and random sampling."Christos Papadimitriou calls it"so hard to believe that it has been discovered five times and forgotten." It has formed the basis of algorithms inmachine learning, optimization, game theory, | ||
