[share_ebook] Discrete Mathematics with Applications

Description

Discrete Mathematics with Applications
Author:
Publisher: Academic Press 2003
Pages: 1042
ISBN: 9780124211803

Preface:
People often ask: What is discrete mathematics? It's the mathematics
of discrete (distinct and disconnected) objects. In other words, it is the
study of discrete objects and relationships that bind them. The geometric
representations of discrete objects have gaps in them. For example, integers
are discrete objects, therefore (elementary) number theory, for instance, is
part of discrete mathematics; so are linear algebra and abstract algebra.
On the other hand, calculus deals with sets of connected (without any
gaps) objects. The set of real numbers and the set of points on a plane are
two such sets; they have continuous pictorial representations. Therefore,
calculus does not belong to discrete mathematics, but to continuous mathematics.
However, calculus is relevant in the study of discrete mathematics.
The sets in discrete mathematics are often finite or countable, whereas
those in continuous mathematics are often uncountable.
Interestingly, an analogous situation exists in the field of computers.
Just as mathematics can be divided into discrete and continuous mathematics,
computers can be divided into digital and analog. Digital computers
process the discrete objects 0 and 1, whereas analog computers process continuous
data~that is, data obtained through measurement. Thus the terms
discrete and continuous are analogous to the terms digital and analog,
respectively.
The advent of modern digital computers has increased the need for
understanding discrete mathematics. The tools and techniques of discrete
mathematics enable us to appreciate the power and beauty of mathematics
in designing problem-solving strategies in everyday life, especially in computer
science, and to communicate with ease in the language of discrete
mathematics.

 

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