COCS-222
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1
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Course number:
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COCS 222
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Name:
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Discrete Structures
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2
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Credits:
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3
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Contact hours:
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42 Hrs. Lecture
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3
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Course coordinator’s name:
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3
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Prof. Dr. Salah Behiry
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4
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a)
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Textbook:
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-Kolman, Ross and Busby, Discrete Math Structure, 6th Edition, Prentice Hall, 2007, ISBN 0132297516.
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b)
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Other references:
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-Ralph. P.Grimaldi, Discrete and Combinatorial Mathematics- An Applied Introduction, 5th Edition, Pearson Education, 2004
-Trembly J.P.& Manohar .P, Discrete Mathematical Structures with applications to computer science, Tata McGraw-Hill Pub Co Ltd, New Delhi, 2007, ISBN-10: 0070651426, ISBN-13: 978-0070651425
-Mott , J.L., Kandel A and Baker T.P., Discrete Mathematics for Computer Scientists & Mathematicians, 2 Sub edition, Prentice Hall, 1986, ISBN-10: 0835913910, ISBN-13: 978-0835913911
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5
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a)
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Synopsis:
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The course aims at teach students basic concept of Discrete Mathematics that enable student to understand the necessary foundations for the study of Computer Science and Information Technology related course.
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b)
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Prerequisites:
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---
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c)
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Type of course:
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Core
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6
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a)
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Course Learning Outcomes:
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Upon finishing this course, the students should be able to:
- Have the knowledge of Discrete Mathematics basics and its applications in Computer Science
- Have the knowledge of basic logic in proof methods
- Understand the number theory and counting basics
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b)
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Student Outcomes:
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This course aims to meet student outcomes (a) and (b) of ABET criterion 3.
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7
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Brief list of topics and their duration
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Number
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Description
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Duration in weeks
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1
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Functions (surjections, injections, inverses, composition)
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1
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2
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Relations (reflexivity, symmetry, transitivity, equivalence relations)
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1
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3
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Sets (Venn diagrams, complements, Cartesian products, power sets)
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1
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4
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Proof Techniques - Notions of implication, converse, inverse, contrapositive, negation, and contradiction. The structure of mathematical proofs and Direct proofs.
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1
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5
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Proof by counterexample and Proof by contradiction. Mathematical induction, Strong induction, Recursive mathematical definitions, Well orderings
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1
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6
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Exam 1
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7
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Basic Logic - Propositional logic, Logical connectives. Truth tables, Normal forms (conjunctive and disjunctive)
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1
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8
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Validity, Predicate logic, Universal and existential quantification
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9
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Modus ponens and modus tollens, Limitations of predicate logic
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1
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10
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Basics of Counting - Counting arguments, Sum and product rule, Inclusion-exclusion principle
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1
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11
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Arithmetic and geometric progressions, Fibonacci numbers, The pigeonhole principle, Permutations and combinations
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1
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12
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Exam 2
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1
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13
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Basic definitions, Pascal’s identity, The binomial theorem,
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1
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14
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Solving recurrence relations, Common examples, The Master theorem
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1
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Final Exam
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8
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Grading System
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Assessment Type
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Percentage of Mark
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Assignment
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15 %
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Quiz
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15 %
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Exam 1
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15 %
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Exam 2
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15 %
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Final Exam
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40 %
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Total
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100 %
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آخر تحديث
12/21/2016 2:27:28 PM
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