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

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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
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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 =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
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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
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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
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11.4 Sum of geometric sequence Theorem. For any real number x = 1 and any integer n 0, n - 1 i =0 x i = 1 - x n 1 - x .
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