Lecture 1 - Introduction. The following will be discussed in this course: Discrete vs continuous, what is discrete structures? Applications of discrete mathematics, logic, elementary number theory and methods of proof, set theory, relations, sequences and recursion, mathematical induction, counting, relations and equivalence relations, graphs, trees. | (CSC 102) Dr. Amer Rasheed COMSATS Institute of Information Technology Discrete Structures Discrete vs Continuous Examples of discrete Data Number of boys in the class. Number of candies in a packet. Number of suitcases lost by an airline. Examples of continuous Data Height of a person. Time in a race. Distance traveled by a car. What is discrete Structures? Discrete mathematics is the part of mathematics devoted to the study of discrete objects (Kenneth H. Rosen, 6th edition). Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous (wikipedia). Applications of discrete mathematics How can a circuit that adds two integers be designed? How many ways are there to choose a valid password on a computer? What is the shortest path between two cities using transportation system? How can I encrypt a message so that no unintended recipient can read it? How many valid internet addresses are there? How can a list of integers be sorted so that the integers are in increasing order? Syllabus (Topics to be covered in this course) Logic Elementary Number Theory and Methods of Proof Set Theory Relations Sequences and Recursion Mathematical Induction Counting Relations and Equivalence Relations Graphs Trees Reference Books Discrete Mathematics and its Applications (with Combinatorics and Graph Theory) 6th Edition, The McGraw-Hill Companies, 2007, Kenneth H. Rosen. Discrete Mathematics with Applications 2nd Edition, Thomson Learning, 1995, Susanna S. Epp. Discrete Mathematics for Computer Scientists 2nd Edition, Addison-Wesley, 1999, John Truss. Logic Propositional Logic Logic of Compound Statements Propositional Equivalences Conditional Statements Logical Equivalences Valid and Invalid Arguments Applications: Digital Logic Circuits Predicates and Quantifiers Logic of Quantified Statements Propositional Logic Proposition: A proposition (or Statement) is a declarative sentence (that is, a sentence that declares a fact) that . | (CSC 102) Dr. Amer Rasheed COMSATS Institute of Information Technology Discrete Structures Discrete vs Continuous Examples of discrete Data Number of boys in the class. Number of candies in a packet. Number of suitcases lost by an airline. Examples of continuous Data Height of a person. Time in a race. Distance traveled by a car. What is discrete Structures? Discrete mathematics is the part of mathematics devoted to the study of discrete objects (Kenneth H. Rosen, 6th edition). Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous (wikipedia). Applications of discrete mathematics How can a circuit that adds two integers be designed? How many ways are there to choose a valid password on a computer? What is the shortest path between two cities using transportation system? How can I encrypt a message so that no unintended recipient can read it? How many valid internet addresses are there? How can a list of integers be sorted .
