% These slides are designed for 52 x 19 terminals % but should work with slightly larger or smaller % terminals. Should be OK with unix "less" and % screens with fewer than 30 lines. Issue /%%etc. % Start at lines 10, 40, 70, 100, etc.; use % vi "set number" and "set nonumber" % line 10: s1%%etc., line 40: s2%%etc., etc. % unix, vi, less -- old school! s0%%% Math 307-101: (0) Announcements (1) Card Shuffling from "6 x 6" to "3 x 3" Sections 0.0 and 0.1. (2) Diagonalize [1/2,1/3;1/2,2/3] (HW 1) you should make sure that you can do this with any reasonable 2 x 2 matrix. (3) Material will be added between Sections 0.1 and 0.2 to help you with sample exam problems. s00%%% Announcements: (1) Homework #1 is set: Problem 1 due Sept 16. Problems 2-6 due Sept 16, unless ugrad lab accounts delayed further. (2) Streamlined homework: - Must be on 8.5 x 11 - Must be stapled upper left - Must have first three letters of last name in clear, block letters - Handed into envelopes by group s7%%% Card Shuffling - Card Shuffling leads to Markov matrices - It is, at times, possible to work with smaller matrices - Start with three cards, A,B,C (6 x 6) - Reduce in two ways to (3 x 3) - Symmetry after first step - Replace A,B,C with A,B,B s8%%% - We need to "review" - Markov matrices - Given (Markov) matrix, A how "to find" A, A^2, A^3,... A^infinity i.e., limit as n-> infty of A^n s9%%% - Review: Eigenvalues and eigenvectors (I make most of my living from them) - Start from first homework problem: - Diagonalize A = [ 1/2,1/3 ; 1/2,2/3 ] Compare 3,000 Solved ... 16.69