Taught: Fall 2007, 2008, Spring 2010, Fall 2010, Spring 2011 2007, 2008, Spring 2009, 2010
The Discrete Mathematics course will be taught from a Computer Science perspective. Chapters were selected to match the needs of students majoring in Computer Science.
We present in chapters 1 and 2 an introduction to both prepositional, predicate logic, rules of inference, basics proof methods, as well as to sets and functions. We introduce in chapter 3, the concept of an algorithm, its properties and some fundamental concepts from number theory, including the division algorithm, prime factorization and congruence. We will cover mathematical reasoning, induction and recursion in chapter 4. We will learn in this chapter various strategies for proving theorems. We will highlight the roles of conjecture and counterexamples. We will show throughout chapter 6 how to develop basic concepts of discrete probability, including conditional probability and expected values. We will show how to use these concepts to study the average case complexity of an algorithm. In chapter 8, we will cover an important discrete structure, namely: the relation. Finally, basic concepts of graph theory (including graph coloring and planar graphs) and its applications will be studied in chapter 9.
Kenneth H. Rosen, Discrete Mathematics and its Applications, Sixth Edition, Mc Graw-Hill, © 2007.