Doerr A., Levasseur K. Applied Discrete Structures

University of Massachusetts, 2016. — 377 p.As a general description one could say that discrete mathematics is the mathematics that deals with “separated” or discrete sets of objects rather than with continuous sets such as the real line. For example, the graphs that we learn to draw in high school are of continuous functions. Even though we might have begun by plotting discrete points on the plane, we connected them with a smooth, continuous, unbroken curve to form a straight line, parabola, circle, etc. The underlying reason for this is that hand methods of calculation are too laborious to handle huge amounts of discrete data. The computer has changed all of this.
Today, the area of mathematics that is broadly called “discrete” is that which professionals feel is essential for people who use the computer as a fundamental tool. It can best be described by looking at our Table of Contents. It involves topics like sets, logic, and matrices that students may be already familiar with to some degree. In this Introduction, we give several examples of the types of problems a student will be able to solve as a result of taking this course.Set Theory
Combinatorics
Logic
More on Sets
Introduction to Matrix Algebra
Relations
Functions
Recursion and Recurrence Relations
Graph Theory
Trees