lec11-connect-sequence

lec11-connect-sequence - EECS 203 Winter 2007 Discrete...

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Unformatted text preview: EECS 203, Winter 2007 Discrete Mathematics Lecture 11 Connectivity, Sequences and Summations February 8 Reading: Rosen [9.4, 2.4] February 8 Connectivity, Sequences and Summations, Page 1 11.1 Matrix multiplication A ∈ R n × k , B ∈ R k × m , then AB = [ c ij ] 1 ≤ i ≤ n, 1 ≤ j ≤ m , and c ij = k X ` =1 a i` b `j . Example: How many multiplications and additions are needed to multiply two n × n matrices? February 8 Connectivity, Sequences and Summations, Page 2 11.2 Counting the number of walks in a graph Let A be the adjacency matrix of a graph G , and r ≥ 1 be an integer. What does A r mean? February 8 Connectivity, Sequences and Summations, Page 3 11.3 Congratulations, you’ve won a lottery! But you need to decide if you want to take $1M today or $50,000 every year for 20 years. February 8 Connectivity, Sequences and Summations, Page 4 11.4 Sum of geometric sequence Theorem. For any real number x 6 = 1 and any integer n ≥ 0, n- 1 X i =0 x i = 1- x n 1- x ....
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This note was uploaded on 04/01/2008 for the course EECS 203 taught by Professor Yaoyunshi during the Winter '07 term at University of Michigan.

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lec11-connect-sequence - EECS 203 Winter 2007 Discrete...

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