ps5 - Probability and Algorithms Leonard J. Schulman...

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Probability and Algorithms Caltech CS150, Winter 2006 Leonard J. Schulman TA: Chih-Kai (Kevin) Ko. Problem set 5 Out Wednesday February 22. Due Monday March 6. Week 6 reading: MU 6.7-6.8, 7.1-7.4, proof of the Perron-Frobenius theorem in notes of Andries Brouwer on the class website. This assignment is longer than usual so I’m allowing two weeks for it. Please get started early though. I haven’t assigned work on the Perron-Frobenius theorem but it is an important theorem with an interesting proof, and well worth learning. (You can also ±nd the proof elsewhere, e.g., some notes online by Mike Boyle.) Exercises: MU 6.16, 6.18, 7.1, 7.6, 7.8, 7.13, 7.17, 7.19, 7.26. Also the following two exercises: (A) Let the van der Waerden function W ( k ) , for nonnegative integer k , be the least nonnegative integer n so that if { 1 , . . . , n } is two-colored, there exists a monochromatic arithmetic progression with k terms. Remarkably, W ( k ) is ±nite for all k ; the upper bound is immense and the true value is far
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This note was uploaded on 01/05/2012 for the course CS 150 taught by Professor List during the Fall '10 term at Caltech.

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