Faculty of Engineering Computer Engineering Department CC 218

Faculty of Engineering Computer Engineering Department CC 218: Discrete Mathematics Introduction Prof. Dr. Amani A. Saad - CC 218 Discrete Mathematics- AAST

WHY SHOULD WE TEACH DISCRETE MATHEMATICS? § Discrete mathematics is the kind of mathematics one needs to know to communicate with a computer as designer, programmer, or user. It is necessary for all students, regardless of their choice of career path. Prof. Dr. Amani A. Saad - CC 218 Discrete Mathematics- AAST 2

WHAT IS DISCRETE MATHEMATICS? § Discrete mathematics includes sets, functions and relations, matrix algebra, combinatorics and finite probability, graph theory, finite differences and recurrence relations, logic, mathematical induction, and algorithmic thinking. Other topics often considered part of discrete mathematics are Boolean algebra, linear programming, and number theory. Prof. Dr. Amani A. Saad - CC 218 Discrete Mathematics- AAST 3

WHAT IS DISCRETE MATHEMATICS? § Because of this diversity of topics, it is perhaps preferable to view discrete mathematics simply as the mathematics that is necessary for decision making in noncontinuous situations. Prof. Dr. Amani A. Saad - CC 218 Discrete Mathematics- AAST

Course Objectives n n n n To introduce students to the fundamental notation and concepts of discrete structures. To engage students in mathematical thinking, reading, writing, and exploration. To develop techniques for proving things about and manipulating discrete mathematical structures. To learn how to develop algorithms and verify their correctness. To introduce students to combinatorial methods and graph theory To develop students’ ability to write clearly and concisely about mathematical ideas and problem solutions. To prepare students for advanced courses in mathematics. Prof. Dr. Amani A. Saad - CC 218 Discrete Mathematics- AAST 5

Course Contents n CH #1: The Logic of Compound Statements. 1. 2. 3. Logical Form and Logical Equivalence. Conditional Statements. Valid and invalid Arguments. n CH #2: The logic of Quantified Statements. 1. 2. Predicates and Quantified Statements. Arguments with Quantified Statements. n CH #3: Elementary Number Theory and Methods of Proof. 1. 2. 3. Direct Proof and Counterexamples I: Introduction. Direct Proof and Counterexamples II: Division into Cases and the Quotient-Remainder Theorem. Indirect Arguments: Contradiction and Contrapositive. n CH #4: Sequences and Mathematical Induction. 1. 2. Sequences. Mathematical Induction. Prof. Dr. Amani A. Saad - CC 218 Discrete Mathematics- AAST 6

Course Contents (Cont. ) n CH #5: Set Theory. 1. 2. Basic Definitions of Set Theory. The empty Set, Partitions, Power set, and Boolean Algebras. n CH #6: Counting. 1. 2. Counting and Probability. Counting Subsets of a Set: Combinations. n CH #7: Functions. 1. 2. Functions Defined on General Sets. One to One and Onto, Inverse Functions. n CH #10: Relations. 1. 2. Relations on Sets. Equivalence Relations. Prof. Dr. Amani A. Saad - CC 218 Discrete Mathematics- AAST 7

References Sussana Epp, Discrete Mathematics with Applications, Mc. Graw. Hill publications. n Kenneth Rosen, Discrete Mathematics and Applications, Thomson Publishers. n Prof. Dr. Amani A. Saad - CC 218 Discrete Mathematics- AAST 8

Staff: n Course Coordinator & Lecturer: ¨Prof. Dr. Amani Anwar Saad ¨ Office hours: Mon 10: 30 - 12: 30 Tues 10: 30 -12: 30 Wed 12: 30 – 2: 00 TA: Eng. Alia Amer Prof. Dr. Amani A. Saad - CC 218 Discrete Mathematics- AAST 9