COCS-222

1

 

Course number:

COCS 222

Name:

Discrete Structures

2

 

Credits:

3

Contact hours:

42 Hrs. Lecture

3

 

Course coordinator’s name:

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Prof. Dr. Salah Behiry

4

a)

Textbook:

-Kolman, Ross and Busby, Discrete Math Structure, 6th Edition, Prentice Hall, 2007, ISBN 0132297516.

 

b)

Other references:

 

-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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a)

Synopsis:

 

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.

 

b)

Prerequisites:

 

---

 

c)

Type of course:

Core

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a)

Course Learning Outcomes:

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

 

b)

Student Outcomes:

This course aims to meet student outcomes (a) and (b) of ABET criterion 3.

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Brief list of topics and their duration

 

Number

Description

Duration in weeks

1

Functions (surjections, injections, inverses, composition)

1

2

Relations (reflexivity, symmetry, transitivity, equivalence relations)

1

3

Sets (Venn diagrams, complements, Cartesian products, power sets)

1

4

Proof Techniques - Notions of implication, converse, inverse, contrapositive, negation, and contradiction. The structure of mathematical proofs and Direct proofs.

1

5

Proof by counterexample and Proof by contradiction. Mathematical induction, Strong induction, Recursive mathematical definitions, Well orderings

1

6

Exam 1

 

7

Basic Logic - Propositional logic, Logical connectives. Truth tables, Normal forms (conjunctive and disjunctive)

1

8

Validity, Predicate logic, Universal and existential quantification

 

9

Modus ponens and modus tollens, Limitations of predicate logic

1

10

Basics of Counting - Counting arguments, Sum and product rule, Inclusion-exclusion principle

1

11

Arithmetic and geometric progressions, Fibonacci numbers, The pigeonhole principle, Permutations and combinations

1

12

Exam 2

1

13

Basic definitions, Pascal’s identity, The binomial theorem,

1

14

Solving recurrence relations, Common examples, The Master theorem

1

 

Final Exam

 

 

8

 

Grading System

Assessment Type

Percentage of Mark

Assignment

15 %

Quiz

15 %

Exam 1

15 %

Exam 2

15 %

Final Exam

40 %

Total

100 %

 



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12/21/2016 2:27:28 PM