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awwalker.com | ||
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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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mattbaker.blog
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| | | | | On Pi Day 2016, I wrote inthis post about the remarkable fact, discovered by Euler, thatthe probability that two randomly chosen integers have no prime factors in common is $latex \frac{6}{\pi^2}$. The proof makes use of the famous identity $latex \sum_{n=1}^\infty \frac{1}{n^2} = \frac{\pi^2}{6}$, often referred to as the "Basel problem", which is also due... | |
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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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4uinews.wordpress.com
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| | | ?? ????? ???? ?? ??????? ???? ?? ???? ???? ?? ????? ?? ????? ????? ?? ????? ???? 1978 ??? ?????? ?? ?? ?? ??? ??? ????? ?????? ?? ???? ???????? ?? ?????? ???? ?? ??? ???? ?? ?????? ?? ?? ???? ??? ?? ???? ??? ?? ????? ??? ??? ?? ???????????? ?? ?? ??? ???... | ||
