Minimal distance to Pi

Given two integers and (), find and print a common fraction such that and is minimal. If there are several fractions having minimal distance to , choose the one with the smallest denominator.

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Nash-Williams' partition theorem

In this exposition, we rewrite the classical proof of the Nash-Williams’ partition theorem so that it resembles that of the infinite Ramsey theorem.

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Hausdorff moment problem

Hausdorff moment problem asks for the necessary and sufficient conditions for a sequence with to be the sequence of the moments of a random variable supported on .

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An uppder bound on the Stirling number of the second kind

We give an upper bound on the Stirling number of the second kind by the probabilistic method.

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A Probabilistic Proof of Isoperimetric Inequality

We demonstrate a probabilistic proof of the isoperimetric inequality.

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On extension of rationals

This note is based on my talk An Expedition to the World of -adic Numbers at Carnegie Mellon University on January 15, 2014.

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Poisson summation and Basel problem

A classical mathematical analysis problem, also known as the Basel problem, first posed by Pietro Mengoli in 1644 and solved by Leonhard Euler in 1735, asks the precise sum in closed form of the infinite series .

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On Thue's method

This note is based on my talk Introduction to Diophantine Approximation at Carnegie Mellon University on November 4, 2014.

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Topological aspects of Hex game

In the previous post, I asserted without proof that the Hex Game will never result a draw. In An Invitation to Discrete Mathematics, Jiri Matousek gave an elegant proof for the assertion, which requires only a little bit of elementary graph theory.

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Communicating through randomness

A room contains a normal 8 by 8 chessboard together with 64 identical coins, each with one “heads” side and one “tails” side. Two prisoners are at the mercy of a typically eccentric jailer who has decided to play a game with them for their freedom.

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