What is Discrete Mathematics? • Study of discrete (as opposed to continuous) objects • Calculus is continuous • Example 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 wining set of numbers in a lottery Kinds of Problems Solved Using Discrete Mathematics • Number of valid passwords • Number of valid websites • Probability of winning a lottery • Link between two computers in a network • Identify spam e-mails • Shortest path • Prove there are infinitely many prime numbers • Numbers of steps need to do a sorting • Prove the correctness of algorithms Goals of a Course in Discrete Mathematics • Mathematical Reasoning • Combinatorial Analysis • Discrete Structures
