lect1 - COT 3100-01 Introduction to Discrete Structures...

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1 COT 3100-01 Introduction to Discrete Structures Instructor: Nadia Baranova [email protected] Office: CCI-216, phone (407) 823-1063 Office hours: M 7p.m.-8p.m., W 2p.m.-3p.m.
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2 Combinatorics and counting technique reading: 1.1-1.4 from the textbook The Rule of Sum If the first event can occur in m ways, the second event can occur in n ways, two events can not occur simultaneously, then either the first event or the second can occur in m + n ways. Example Suppose for graduation you need to take one course in any programming language. There are 10 courses offered in CS and 5 courses in EE. How many choices do you have? n =10, m =5, n + m = 15
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3 The Rule of Product If something can happen in n ways, and no matter how the first thing happens, a second thing can happen in m ways, then two things together can happen in n·m ways.
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4 A bit (or binary digit) is a zero or one. A bit string is defined to be a sequence of bits. Different symbols can be encoded by bit strings. Suppose we want to encode 26 letters of the English alphabet. Is it sufficient to use one and two bit strings? Here they are: 0, 1, 00, 01, 10, 11- only six different strings. Example 0 1 first 0 1 0 1 second 00 01 10 11 four 2-bit strings
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5 How many 3 bit strings exist? 2 × 2 × 2=8 first second 0 1 0 1 0 1 0 1 0 1 0 1 0 1 third
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DNA is a chain of 4 bases: T, C, A and G. How long the chain should be to encode one of 20 existing amino acids?
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lect1 - COT 3100-01 Introduction to Discrete Structures...

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