After reading the material in this chapter, you should be able to: What is discrete mathematics? Kinds of problems solved using discrete mathematics, goals of a course in discrete mathematics, discrete mathematics is a gateway course. | Discrete Mathematics and Its Applications Introductory Lecture Copyright © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. What is Discrete Mathematics? Discrete mathematics is the part of mathematics devoted to the study of discrete (as opposed to continuous) objects. Calculus deals with continuous objects and is not part of discrete mathematics. Examples of discrete objects: integers, steps taken by a computer program, distinct paths to travel from point A to point B on a map along a road network, ways to pick a winning set of numbers in a lottery. A course in discrete mathematics provides the mathematical background needed for all subsequent courses in computer science and for all subsequent courses in the many branches of discrete mathematics. Kinds of Problems Solved Using Discrete Mathematics How many ways can a password be chosen following specific rules? How many valid Internet addresses are there? What is the probability of winning a particular lottery? Is there a link between two computers in a network? How can I identify spam email messages? How can I encrypt a message so that no unintended recipient can read it? How can we build a circuit that adds two integers? Kinds of Problems Solved Using Discrete Mathematics What is the shortest path between two cities using a transportation system? Find the shortest tour that visits each of a group of cities only once and then ends in the starting city. How can we represent English sentences so that a computer can reason with them? How can we prove that there are infinitely many prime numbers? How can a list of integers be sorted so that the integers are in increasing order? How many steps are required to do such a sorting? How can it be proved that a sorting algorithm always correctly sorts a list? Goals of a Course in Discrete Mathematics Mathematical Reasoning: Ability to read, understand, and construct mathematical . | Discrete Mathematics and Its Applications Introductory Lecture Copyright © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. What is Discrete Mathematics? Discrete mathematics is the part of mathematics devoted to the study of discrete (as opposed to continuous) objects. Calculus deals with continuous objects and is not part of discrete mathematics. Examples of discrete objects: integers, steps taken by a computer program, distinct paths to travel from point A to point B on a map along a road network, ways to pick a winning set of numbers in a lottery. A course in discrete mathematics provides the mathematical background needed for all subsequent courses in computer science and for all subsequent courses in the many branches of discrete mathematics. Kinds of Problems Solved Using Discrete Mathematics How many ways can a password be chosen following specific rules? How many valid Internet addresses .
