Introduction to Discrete Structures
Introduction to Discrete Structures COT 3100
University of Central Florida
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This 2 page Class Notes was uploaded by Lamont Block on Thursday October 22, 2015. The Class Notes belongs to COT 3100 at University of Central Florida taught by Sean Szumlanski in Fall. Since its upload, it has received 90 views. For similar materials see /class/227688/cot-3100-university-of-central-florida in Engineering and Tech at University of Central Florida.
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Date Created: 10/22/15
Course Description COT 3100 Introduction to Discrete Structures Spring 2008 Designation COT3100 is required for CS majors Catalog Description Logic sets functions relations combinatorics graphics Boolean algebras nitestate machines Turing machines unsolvability computational complexity Pre requisite Courses MAC 1105 MAC 1114 Textbooks and References Required textbook Discrete arid CombinatorialMathematics 539h ed by Ralph P Grimaldi Addison Wesley 2003 ISBN 0201726343 Course Learning Outcomes and Expected Performance Criteria Course Outcomes Measures Threshold Outcome 1 Student shall be able to apply formal methods of Embedded Questions on symbolic propositional and predicate logic to describe how Q21 Q22 Q23 Hwkl 67 formal tools of symbolic logic are used to model algorithms Hwk5 Exml Exm3 and reallife situations and to use formal logic proofs and logical reasoning to solve problems Outcome 2 Student shall be able to demonstrate basic Embedded Questions on counting principles including the pigeonhole principle and to Q23 Q24 Q25 Hwkl 67 compute permutations and combinations of a set and interpret Hwk2 Hwk3 Hwk4 the meaning in the context of the particular application Hwk5 Hwk6 Exml Exm2 Exm3 Outcome 3 Student shall be able to outline the basic structure Embedded Questions on of and give examples of direct proof proof by contradiction Q27 Hwkl Hwk2 67 disproof by counterexample and proof by contraposition to Hwk4 Hwk5 Hwk6 discuss which type of proof is best for a given problem to Exml Exm2 Exm3 relate the ideas of mathematical induction to recursion and recursively defined structures and to identify the difference between mathematical and strong induction and give examples of the appropriate use of each Outcome 4 Student shall understand basic principles and Embedded Questions on techniques of number theory including the Euclidean Q29 Hwkl Hwk4 67 algorithms related to the greatest common divisor of two Exml Exm2 Exm3 integers Outcome 5 Student shall be able to explain with examples the Embedded questions on basic terminology of functions relations and sets to perform Q210 Qzll Q212 67 the operations associated therewith and to relate practical Hwk2 Hwk3 Hwk5 examples to the appropriate set function or relation model Hwk6 Exml Exm2 and interpret the associated operations and terminology in Exm3 context Note It is expected that 50 ofall students passing this course shall meet or exceed the performance threshold on each Outcome Topics Covered Symbolic and predicate logic the Laws of Logic and Rules of Inference and logic proofs also modeling realworld problems with formal propositional logic 2 Counting principles including permutations combinations and the pigeonhole principle 3 Methods of proof including direct proofs proof by contradiction proof by contraposition proof by induction and disproof by counterexample 4 Number theory including diVisibility theorems prime numbers prime factorization Euclid s Second Theorem and Euclid s algorithm for nding the greatest common diVisor of two numbers 5 Functions relations and set theory including partial ordering relations binary closures of relations equivalence relations and equivalence classes function and relation compositions injections surjections and bijections and function inverses V Class andor Laboratory Schedule Number of sessions per week 3 2 lecture sessions and 1 lab session per Duration of each session 2 of 75 minutes 1 of 50 minutes Contribution of course to meeting the Professional Component Math amp Science Topics 3cr Engineering Topics 0cr General Education Topics 0cr Relationship of the course to the Degree Program Outcomes I BSCS Program Outcome 1 All graduating CS majors shall demonstrate their knowledge of discrete and continuous mathematics and their ability to apply logic and mathematical prooftechniques to computing problems addressed by course outcomes 15addresses CACa BSCpE Program Outcome 13 Graduates of the ComputerEngineen39ng program should attain a knowledge of discrete mathematics addressed by course outcomes 15 I BSEE Program Outcome 13 Graduates of the Electrical Engineering program should attain a knowledge of advanced mathematics typically including di erential equations linear algebra and complex variable addressed by course outcome 15 Prepared by Sean Szumlanski Date May 30 2008
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