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Discrete math is the opposite of continuous math. Much of your experience in math has been continuous in nature. In our number
system, there is always a number between any two numbers (i.e. between 2/7 and 3/7 is the number 5/14 ) and between any two
points on a line there exists at least one other point. In discrete math these events do not occur. The set of points { .
. . . . . . . } is discrete (i.e. there are two points next to each other with no point between them). The set of counting
numbers is discrete. There is no counting number between 7 and 8. The problems we will be studying in this course will involve
applications of discrete sets.
Discrete mathematics is a rapidly growing and increasingly used area of mathematics with many practical and relevant applications.
It deals with complex problem solving in a variety of fields ranging from networking and telecommunications to cryptanalysis,
social choice theory, statistics, and operations research. The specific mathematics that is used involves learning the following
topics in detail:
* Combinatorics
* Voting and weighted voting theory
* Fair division algorithms
* Graph theory (networking and minimum paths)
* Population dynamics
* Chaos theory
* Fractal geometry
* Linear programming (graphical and matrix solutions)
* Statistical analysis.
All of these topics will be introduced and studied from the standpoint of numerical analysis, algebraic manipulation skills,
geometric/graphical interpretation, and through the written word. Computer and calculator usage is an integral part of the
course. Working with spreadsheets and other math programs enables each student to analyze the course material and arrive at
his/her own conclusions with sufficient justification.
Many colleges have been offering courses in discrete mathematics for the past twenty-five years. The course was originally
designed for the computer science major as an application of finite mathematics, but has been adapted by the business department
and renamed managerial science or operations research.
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