Syllabus - CSE 1400 Applied Discrete Mathematics or MTH...

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CSE 1400 Applied Discrete Mathematics or MTH 2051 Discrete Mathematics Class Syllabus Department of Computer Sciences College of Engineering Florida Tech Fall 2011 Abstract Student Name Attributes Calendar Events Type Material Readings Problems Policy Rules Rewards Topics Ideas Skills Outcomes Assessment Level Professor Name Attributes Grade A–F Assistant Name Attributes 1 ..* Measures Learning 1 ..* 1 ..* Learns from 1 1 ..* Achieves 1 ..* Follows Studies 1 ..* Determines 1 Establishes 1 Assigns * Teaches 1 Covers 1 ..* Includes Includes * Helps 1 * Helps 1 ..*
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syllabus 2 Purpose of the Course The emphasis is on algorithmic problem-solving. Algorithmic effi- ciency, elegance, and generality are important characteristics. The course prepares students to solve problems in computing with applications in business, engineering, mathematics, the social and physical sciences and many other fields. Students study discrete, finite and countably infinite structures: logic and proofs, sets, nam- ing systems, in particular, number systems, relations, functions, se- quences, graphs, and combinatorics. These topics are commonly used to reason about problems and to develop correct algorithmic solutions for them. Course Outcomes By the end of the course, each student will be able to 1 . The decimal number 15 can be written as ( 15 ) 10 = ( 1111 ) 2 = ( 01111 ) 2 c = ( F ) 16 2 . x = x X . 3 . For all natural numbers n 0 k < n 2 k = 2 n - 1 4 . For all sets X and Y , X Y = X Y . 5 . If p = False , q = False , and r = True , then ( p q ) ( ¬ p r ) = True . 6 . You can fool some of the people all of the time, and all of the people some of the time, but you cannot fool all of the people all of the time. ( p )( t )( canfool ( p , t )) ( p )( t )( canfool ( p , t )) ( p )( t )( ¬ canfool ( p , t )) . ( 1 ) 7 . is a partial order on 2 X partial orders and equivalence relations. 8 . Using an O ( n lg n ) sorting algo- rithm. a million things can be ordered in about 20 million steps. 9 . There are ( n k ) k -elements subsets of an n -element set. 10 . P = { 2, 3, 5, 7, 11, . . . } , gcd ( 51, 24 ) = 1, 3 x = 4 ( mod 5 ) = x = 3. 1 . Use several systems to name numbers; employ algorithms to convert between these systems; and compute the number of things that can be named in a system as a function of its alphabet size and the length of numeral strings. 2 . Recognize valid and invalid arguments. 3 . For simple propositions about the natural numbers, correctly complete proofs by induction.
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